Is there a temperature which you cannot exceed like you cannot go below 0 Kelvin?

First of all, temperature is just a type of energy. The reason absolute zero is absolute zero is because the atoms have effectively stopped moving and have no kinetic energy.

I would suspect the maximum temperature on earth would be attained inside a particle accelerator (aka. “atom smasher”). Upon impact, the individual atoms have so much energy or that they literally tear themselves apart, rearrange with other atoms, and do all sorts of bizarre things.

As to pegging a “temperature” number to these kinds of reactions, I don’t think a “degree number” would really give you a valid or meaningful description of how much energy is present.

Short answer: I would say there’s no maximum temperature (for all intents and purposes). HOWEVER, the atoms are limited in their internal strength at at some “temperature” E=MC2 applies and the mass will convert to energy.