I posted below a link to a similar question about the why c is the limiting speed.  This question tries to relate temperature to the concept of time dilation (of course, I realized that the obvious gist is to consider that higher temperature means higher velocity and thus higher time dilation for the speeding particles). That is narrow and imprecise since temperature is defined by a distribution.  Instead I will provide another view of time dilation. 

In my theory (Hypergeometrical Universe Theory or HU), time flows normally. What changes is that the laws of physics are velocity dependent, or more specifically, they are Fabric of Space (FS) local torsional state dependent. You will see some pictures representing the tilting of the local FS due to interaction. Interaction happens through a dilaton field that propagates at Sqrt(2) c. At each de Broglie step, a new position for the dilator (matter) is calculated with respect to the normal to the local surface. As the local surface tilts towards 45 degrees, the value of position change becomes smaller and smaller.  That value corresponds to an acceleration and thus Forces become weaker and weaker.

Since forces are what drive chemistry, life, perception, this is equivalent to FREEZING the traveling Twin in Einstein's Twin Paradox.  This means that in HU, time dilation is exactly FREEZING and I will never become rich and famous for writing a book about time, since it can be summarized in a sentence. - No amazing insight there...:)

https://www.quora.com/%E2%80%9CWhy%E2%80%9D-is-light-speed-the-fastest-thing-in-the-universe/answer/Marco-Pereira-1

Temperature can represent vibrational energy and rotational energy, not just translational energy, (1/2)kT per degree of freedom.

There is a relation to relativity, but not a one to one correspondence of temperature with time dilation.

At higher temperatures, molecular thermal kinetic energy is greater, so if is the average magnitude of the velocity, i.e, the average speed, of thermal motion, as observed in the lab reference frame this corresponds to time as experienced by the molecules being slowed down by a factor of (1 - ^2/c^2)^1/2. At ordinary temperatures

@ RG scholars;;;;;

we know that the early universe is so hot...then what is  its (Temperature ) effect on calculating the age of the present universe and not only age but also different aspects?

@Remi Cornwall...  Does it even make sense to speak of a billionth of a trillionth of a second after the Big Bang when current Cosmology doesn't have an "Unified Force" to describe dynamics?  Isn't stretching speculation a little too thinly...:)

On every other aspect of Cosmogenesys or initial Cosmodynamics, one uses absolute time as opposed to proper time.

@Remi Cornwall;;;

thank you...

as said by Marco Pereira(in above) in describing dynamics ..proper time has to be change...of course proper time means the time measured by the particle by its own watch...

for example say; the Earths gravity is increased by increasing its density..what happens to its proper time? 

@ Dr. Hussainsha,

Good thinking.

The question has been discussed thoroughly in a couple of excellent papers. One at hand is:

D. ter Haar and H. Wergeland, "Thermodynamics and Statistical Mechanics in the Special Theory of Relativity". Physics Reports [Physics Letters (Section C)], 1C (2), (1971), 31-54.

Regards.

@ Humam B. Ghassib 

thank you

Firstly, I think the fact that specific heat capacity is defined for bulk solids renders the final result (equation (8)) inapplicable. How does one explain the final result (in particular, specific heat) for an elementary particle (eg. a fermion or boson) in relativistic motion?

Secondly, any kind of work done involves heat as a by-product of the primary process (eg., consider the following types of work done - Fdx, pdV, −B · dμ, −E · dp), hence, the work-energy theorem (as employed by the author) doesn't take into acount the primary work done, and only considers the heat generated.

Any inputs would be appreciated! Thank you