The so-called Unruh temperature follows from an incorrect equivalence between the phase of the wave function as being given by the ratio of the classical action to Planck's constant and the Boltzmann factor, or the ratio of the energy to the thermal energy. Forgetting that one is a phase and the other a real exponential decaying factor, we place ourselves at the origin of the coordinate system so the action is the product of the energy and time. The unfounded equivalence then gives the acceleration as the ratio of the velocity of light to time, and, consequently, the absolute temperature proportional to the latter. The incomprehensible result would mean that there would be zero temperature in an inertial system, contradicting what we know about the temperature being proportional to the average kinetic energy by which the molecules move about. The same remarks also apply to the Hawking temperature where the acceleration is identified as gravitational acceleration.
According to the Wikipedia definition, "It is the prediction that an accelerating observer will observe black-body radiation where an inertial observer would observe none. In other words, the background appears to be warm from an accelerating reference frame; in layman's terms, a thermometer waved around in empty space will record a non-zero temperature. The ground state for an inertial observer is seen as in thermodynamic equilibrium with a non-zero temperature by the uniformly accelerated observer."
Apart from the fact that "inertial" and "uniformly accelerated" are two different, and incompatible, states of motion, the fact that 'waiving a thermometer around picks up a finite temperature says it all'. And what it has to do with black body radiation? It should be valid for all systems or none.
All the way around, and regardless of thermodynamics, the equivalence principle ensures there is no fundamental difference between acceleration and gravity. The question of Unruh temperature boils therefore down to the existence of Hawking radiation in black holes. In fact, locally any gravitational field is approximately equal to the centrally symmetric field of a far black hole. If the latter have a temperature (and therefore radiate) then the equivalence principle ensures existence of Unruh radiation. Now, black holes have an energy. Then, they have a temperature provided they have an entropy. Now, let us suppose such entropy does not exist. In front of a black hole, I am free to enjoy my last seconds of life having a nice cup of Italian coffee. A kind waiter brings the coffee and the sugar. But I am afraid of the imminent death, so my shaking hand lets both the the cup of coffee and the sugar fall down into the black hole. Now, if I have stirred the sugar inside the coffee before letting the cup fall into the black hole then the state of the Universe differs from what it would have been had I not mixed sugar and coffee before the fall. If the black hole has no entropy, then I have allowed it to destroy entropy just by letting a cup of sweetened coffee fall into the black hole. Following Beckenridge, I am therefore forced to assume black holes have entropy, hence temperature. Unruh follows.
The equivalence principle is hardly a principle. Just take the Beltrami metric for the Poincare' disc model. The radius of the disc is determined by the ratio of the angular velocity to the speed of light. Since this appears as a squared term in the denominator of the hyperbolic metric, you can replace square of the angular velocity by the gravitational potential. [this is what is done in the transition from the inner to the outer Schwarzschild solution, which makes it physically meaningless]. But then what was a metric of constant [negative] curvature has now become a metric of non-constant curvature! So gravity and acceleration are not equivalent by any means [A New Perspective on Relativity (World Scientific, 2011), p. 431.]
One should also be careful to deduce new conclusions from 'gedanken' experiments. The input is exactly equal to the output so that nothing can be learned from such 'experiments'.
There is only one system that radiates with a black-body spectrum, and that is a black body. The absolute temperature has nothing to do with accelerations, and thermodynamics holds that if it is true for one system then it is true for all systems. The same structure of black body radiation does not hold for black holes. If you assume the validity of the Bekenstein form of the entropy and the Hawking expression for the temperature, then you will find that the former violates the second law of thermodynamics, while the latter violates the third law. The entropy of a black body is proportional to the internal energy raised to the power 3/4--not to the square of the energy. The energy of a black body varies as the fourth power of the temperature---and not the inverse of the temperature.
As for the equivalence principle, indeed, it is rather a fact than a principle: no experimental way is yet known to make locally a distinction between gravitational and inertial forces. Here I stress the word 'locally'. To an observer located inside a free-falling elevator the space-time appears to be flat; remarkably, the linear size of the elevator is
Concerning the absolute temperature and accelerations, you need not look further than Einstein's 1912 derivation of the bending of light rays in a gravitational field. He started with the longitudinal Doppler shift for the frequency. He then replaced the velocity by the gravitational acceleration times time, thereby contradicting that the system was ever inertial. He further introduced the static gravitational field, by replacing time as the ratio of the height that a photon will travel to the speed of light in the given time. Thus, he went from an inertial frame to one of uniform acceleration--and finally-- to one of a static gravitational field. General relativity suffers from the same type of hodgepodge.
How then can a static gravitational field make a uniformly rotating disc disappear? The centrifugal forces are contained even in a flat space metric--gravitational forces not.
The same applies to the relativistic expression for the temperature in an inertial system. Once you introduce the virial theorem for converting the kinetic energy into some other form of energy you change functional dependencies and the physics.
Have no fear that the neither the temperature of a black hole nor its entropy will ever measured. That's the difference between Planck's confirmation of his theory and what Bekenstein (not Beckenridge) and Hawking have done. Planck had the data at hand, Bekenstein and Hawking not. And even if they did have the data it show that their expressions are blatantly wrong. The entropy cannot increase faster (or equal to) the first power of the energy, and the energy cannot increase as the temperature decreases.
As for the light bending, there is no need to invoke inertial systems. Indeed, the whole effort of Einstein aims precisely at systems which are far from inertial. Geberal relativity aims at writing the laws of physics in the same way for all observers, inertial and not.
In particular, the equivalence principle made Einstein to replace velocity with the product of acceleration g and time t, as far as he focussed his attention on (Earth's) uniform gravitational field. Given the equivalence principle, he had no other choice. Planck's proportionality between photon frequency and photon energy fits nicely this scenario, as it allows generalisation to 4-dimensional space-time.
As for the centrifugal forces, the fact that they are not distinguishable from gravity is the basic fact of all 'artificial gravity' proposal in astronautics, since Von Braun's times.
As for future measurements, let the future speak for itself. Of course, it is perfectly possible that the equivalence principle is wrong. However, should Hawking and Beckenstein (sorry for the misprint) be wrong, the question of the cup of coffee with/without sugar would remain unanswered. Free fall beyond the event horizon is something irreversible for all practical purposes, and irreversibility means that entropy increases somehow.
P.S. Again, all this discussion of mine holds locally and only locally. In Einstein's gedanken experiment gravitational acceleration is uniform (and replacement of velocity by g times t makes sense) as far as Earth's field is uniform, i.e. as far as the region concerned by measurements is small enough. Personally, I find this similarity with familiar, non-relativistic systems at local thermodynamic equilibrium quite striking: both general relativity and local thermodynamic equilibrium deal with the evolution of a small mass element of fluid along its own line of universe. It seems like the decade-old General Evolution Criterion allows some generalisation to general relativity.
You can't use the equivalence principle to replace velocity by the gravitational acceleration times time. The Doppler principle works for inertial systems, and introducing gravitational acceleration, or any acceleration at all, will destroy the principle so that there can be no justification in the end result.
To see the speciousness of Einstein's reasoning, just consider his remarks on the uniform rotating disc, which Stachel calls the 'missing link' in his formulation of his general theory. Einstein concludes that clocks should go slower on the periphery of the disc. He was clearly not aware of the fact that the rotating disc doesn't belong to the realm of Euclidean geometry: There is no measurement on the disc that would allow on to mark his spot on the disc. All points on the disc are the same to the local inhabitants [Sec. 9.1]. The same holds for his remarks on linear spatial contraction versus rotation.
And if that isn't bad enough just look at the metrics that general relativity uses; for example (111.12) of Landau and Lifshitz, Classical Fields. What they consider as the radial coordinate is actually the circumference of a hyperbolic circle [p. 487 NPR]!
There is also much to criticize about the hypothesis of local thermodynamic equilibrium in nonequilibrium processes [cf. Generalized thermodynamic potentials and universal criteria of evolution, Lettere al Nuovo Cimento 3 (1972)
385-390].
Only the relative velocity of observer and source can cause a Doppler effect. And there is a difference between the Doppler effect for sound and light. Because the speed of light is constant for all observers, the frequency and wavelength must both vary in order to maintain c constant. There is no such condition for water waves, acoustic waves, etc. The wavelength can be maintained constant and the frequency varied, for instance.
The Doppler effect has nothing whatsoever to do with acceleration, as anyone who received a speeding ticket knows. It may make sense to ask whether a body in motion relative to another body appears hotter or colder, but it make no sense to ask whether an accelerating body is hotter or colder. And it is even more ridiculous to believe that their temperatures vanish with their accelerations, instead of becoming equal as in the inertial case.
You can't apply Lorentz transforms to a uniformly rotating disc. That the circumference of a uniformly rotating disc is greater than its Euclidean value has not whatsoever to do with the Lorentz contraction of the radius, as Einstein believed.
The section you refer to in Classical Fields treats radiation from a moving charge. The analysis by Lienard and Wiechert pre-dates relativity. And its relation to the Beltrami metric is clear [NPR eqn (4.3.16)]. The Beltrami metric is related to the energy loss in a frame that is moving with the electron. Since it is the metric of a uniformly rotating disc (this time with charge) it does not come under the jurisdiction of Lorentz transforms---not even local ones.
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