The concept of Debye temperature came from the attempt to understand the temperature dependence of specific heat by the Debye theory that approximate the phonon density of states by the Debye function. The Debye function, although a significant improvement from the simple Einstein function, is still a crude approximation of the real phonon density of states. So the Debye temperature obtained from the fitting the specific heat data should be considered as a fit parameter of an approximate theory. So a single Debye temperature does not often reproduce the specific heat properly at all temperature and therefore temperature dependence has to be considered. Again Debye-Waller theory of the intensity variation of the Bragg peaks at a finite temperature as a function of momentum transfer Q need a factor B which is called Debye-Waller factor. It is also possible to determine Debye temperature by the Q dependence of the Bragg intensities. If you measure Debye temperature by X-ray method then it will not be exactly what you will find from fitting the temperature dependence of the specific heat. But this is not a real contradiction. It is just the outcome of fit parameters of approximate theories. You can do much better if you know  either by calculations or inelastic neutron scattering the real phonon density of states and then calculate the Debye temperature from the moments of the phonon density of states. All the necessary eauations can be found for example from the book, Theory of Lattice Dynamics in harmonic approximation, A.A. Maradudin, E.W. Montroll and G.H. Weiss, Academic Press (1963).

There are some "indirect" methods (Mossbauer & Raman spectra). The best way is, of course, to determine it directly from cp (cv) vs. temperature data (adiabatic calorimetry or DSC). One, rather improvised method, is based on the mass of evaporated LN2 (http://scitation.aip.org/content/aapt/journal/ajp/60/5/10.1119/1.16894). I think that any "rule of thumb" can be quite missleading in this case. Even directly (from cv vs. T) determined values of T_Deb are often quite different one of each other. If the debye theory cannot describe the cv vs. T dependence in a satisfacory way in the whole range of temperatures, then, as usually, an artificial T_Debye vs. T dependency can be introduced. It always depends on the available data.

One can also use the Electro spin resonance, an alternative possibility to determine Debye temperature of compounds.

http://arxiv.org/ftp/cond-mat/papers/0501/0501017.pdf

As described above:

Direcrtly from Cp temperature dependence measurements.

Or estimate it from Mandelstam-Raman & Mossbauer  spectra.

If you want a theoretical rule of thumb (which is however really quite rough) you can use the Lindemann melting criterion which relates the melting temperature of a material linearly with its Debye temperature.  

Just a random reference with Lindemann's equation:

http://onlinelibrary.wiley.com/doi/10.1002/pssa.2210350152/abstract

I think that from theoretical point of view definition of the Debye temperature in the case of compounds is tricky. The point is in the phonon spectrum of compounds there are not just acoustical modes, but also the optical ones. The Debye model is intended to describe acoustical modes, so when calculating the Debye temperature from Cp, we obtain something like effective Debye temperature. It can be different from the Debye temperature defined as corresponding to the highest frequency of the acoustical part of the phonon spectrum, which can be calculated or measured e.g. by INS. On the other hand, as long as we define the Debye temperature itself as a quantity, which provides the best agreement between experimental heat capacity and the one calculated using the Debye model (forget about the electron contribution to heat capacity for a while) , I think, this approach is correct…

The concept of Debye temperature came from the attempt to understand the temperature dependence of specific heat by the Debye theory that approximate the phonon density of states by the Debye function. The Debye function, although a significant improvement from the simple Einstein function, is still a crude approximation of the real phonon density of states. So the Debye temperature obtained from the fitting the specific heat data should be considered as a fit parameter of an approximate theory. So a single Debye temperature does not often reproduce the specific heat properly at all temperature and therefore temperature dependence has to be considered. Again Debye-Waller theory of the intensity variation of the Bragg peaks at a finite temperature as a function of momentum transfer Q need a factor B which is called Debye-Waller factor. It is also possible to determine Debye temperature by the Q dependence of the Bragg intensities. If you measure Debye temperature by X-ray method then it will not be exactly what you will find from fitting the temperature dependence of the specific heat. But this is not a real contradiction. It is just the outcome of fit parameters of approximate theories. You can do much better if you know  either by calculations or inelastic neutron scattering the real phonon density of states and then calculate the Debye temperature from the moments of the phonon density of states. All the necessary eauations can be found for example from the book, Theory of Lattice Dynamics in harmonic approximation, A.A. Maradudin, E.W. Montroll and G.H. Weiss, Academic Press (1963).

TDebye~  (0.2 ~ 0.3) xTmelting

A detailed answer is given in the pdf-file.