"The answer a typical physicist gives to the question, "what is the highest possible temperature?" will depend on their implicit opinion of the completeness of our current set of physical theories. Temperature is a function of the motion of particles. If the speed of light is the universal speed limit, then a gas of maximum temperature may be defined as a gas whose atomic constituents are each moving at the speed of light. The problem is that attaining the speed of light in this universe is impossible; light speed is a quantity that may only be approached asymptotically. The more energy you put into a particle, the closer it gets to moving at light speed, though it never fully approaches it.

At least one scientist has proposed defining the maximum possible temperature as what we would get if we took all the energy in the universe and put it into accelerating the lightest possible particle we could find as closely as possible to the speed of light. If this is true, then discoveries about elementary particles and the size/density of the universe could be relevant to discovering the correct answer to the question this article addresses. If the universe is infinite, there may be no formally defined limit to the maximum possible temperature.

Even though infinite temperature may be possible, it might be impossible to observe, therefore making it irrelevant. Under Einstein's theory of relativity, an object accelerated close to the speed of light gains a tremendous amount of mass. That is why no amount of energy can suffice to accelerate any object, even an elementary particle, to the speed of light - it becomes infinitely massive at the limit."

(It continues to state "If a particle is accelerated to a certain velocity near that of light, it gains enough mass to collapse into a black hole, making it impossible for observers to make statements about its velocity. That is why the Planck temperature is often referred to as the maximum possible temperature"... But that is wrong by the way, well, as far as I know. The correct definition for how a Black hole can come to be is one thing, and one thing alone. ..Compression.. and the 'massiveness' referred too above is the 'relative mass' or 'momentum' of the particle, not that its 'invariant mass' ('real mass', sort of) grows.)

So do a black hole radiate?

No, if we ignore its possible Hawking radiation a black hole should be very cold. Why, because all radiation have only 'one way' to its center. And how did it reach that 'absolute coldness'? By compression turning all matter into 'radiation', and then 'energy'.

So how much 'energy' does it take?

Absolute 'cold', and absolute 'heat'?

Look at a black hole