This suggestion of mine can also be used for
any of you on this site who may be seeking a
subject for a doctorate thesis in Physics.

The late Isaac Asimov asked the question.

Others have asked the question as well.

QUESTION: If "absolute zero" is the bottom limit for temperature,
what is the top limit, if any?

ANSWER: There must be an upper limit to temperature in the physical universe because....

Two well-known physical properities in the universe have asymptotic limits.

(1) The speed of light: C.
(2) Lowest temperature limit: Absolute zero.

As physical asymptotes, an object can approach to with a sliver of the speed-of-light or
the temperature absolute zero, but never reach such values.

So it must be with the highest-temperature possible.

The highest temperature possible is dependent on how much energy a given mass
can contain....And that is related to Einstein's equation E = MC^2.
It's also dependant on the Specific Heat capacity of any given substance or mass, S(h),
as defined in this well-known but simple thermodynamics equation.
He = M x S(h) x T

He = heat energy.
M = mass [usually grams]
S(h) = Specific Heat [cgs metric units]
T = temperature [Celsius or Centigrade]

Since we'll use grams for mass value, then a gram of matter can ONLY contain
9.0 x 10^20 ergs of energy / gram according to Einstein's famous mass-energy equation...

Then, by derivation of that theromodynamics equation, inserting in the upper energy-limit value, we get....
He / M = S(h) x T = 9.0 x 10^20 ergs.

That means? ....T (temperature) would have an Upper limit...an upper limit dependent
on the Specific Heat capacity value [a value which cannot be infinite, as well]