There is no agreed-upon value, among physicists, for a maximum possible temperature. Under our current best-guess of a complete theory of physics, the maximum possible temperature is the Planck temperature, or 1.41679 x 10^32 Kelvins. This translates to about a quarter of a hundred nonillion degrees Fahrenheit (2.5 x 10^32). However, it is common knowledge that our current theories of physics are incomplete, thus leaving open the possibility of still higher temperatures.

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. 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.

The Planck temperature is reached in this universe under at least two separate conditions. The first occurred only once, one Planck time (10^-43 seconds) after the Big Bang. At this time, the universe existed in an almost perfectly ordered state, with near-zero entropy. It may have even been a singularity, a physical object that can be described by only three quantities; mass, angular momentum, and electric charge. But the 2nd Law of Thermodynamics insists that the entropy (disorderliness) of a closed system must always increase. This means that the early universe had only one direction to go--that of higher entropy--and underwent a near-instantaneous breakdown, momentarily producing the Planck temperature.

The second set of conditions capable of producing the Planck temperature are those occurring at the final moments of a black hole's life. Black holes evaporate slowly due to quantum tunneling by matter adjacent to the black hole's surface. This effect is so slight that a typical black hole would take 10^60 years to radiate away all its mass, but smaller black holes, like those with the mass of a small mountain, may take only 10^10 years to evaporate. As a black hole loses mass and surface area, it begins to radiate energy more rapidly, thereby heating up, and at the final instant of its existence, radiates away energy so quickly that it momentarily achieves the Planck temperature.