I found an answer to my own question. The quote is from
"Is there an absolute maximum temperature?"
We posed this question to Sam Gregson, High Energy Particle Physicist at the University of Cambridge...
The temperature of a system is simply related to the amount of energy in that system. Because the system can't have a negative energy, there is only so much heat you can remove from it and so a limit to how cold you can get. This is called absolutely zero. We’ve got very close to it. Scientists in Finland have cooled rhodium atoms to a 10th of a billionth of a degree above absolute zero. On the other hand, an absolute maximum temperature would require there to be a limit to the amount of energy you can give to a particle. As far as we know, there is no such limit.
Although the speed of light is the universal speed limit, the reason you can't get there is that this would require an infinite amount of energy. So this speed limit does not limit the amount of energy and therefore, the temperature of an individual particle.
The most energetic particle ever observed was a cosmic ray over Utah, travelling at 99.999999999985% of the speed of light. Probably a single proton with about 50 joules of energy. This is equivalent to about 5 trillion trillion degrees Celsius and there is no evidence that this is the hottest you could get to.
As far as we know, you are just limited by the amounts of energy you can give to a particle. So you could say that the absolute maximum temperature is a temperature equivalent to all the energy in the universe, concentrated onto one particle. But that limits more accounting than basic physics.
Thanks, Sam Gregson from Cambridge and CERN. So temperature is related to thermal energy and Einstein’s theory of relativity means that although a particle has a universal speed limit, it doesn’t have an energy limit. If you took all of the energy in the universe and put it into one particle, you'd essentially run out of energy before you run out of capacity for energy which is why we have no absolute maximum temperature.