Absolute zero...is there an absolute maximum temperature?

No but at some level the energy would be so great that relativity or quantum mechanics might play a role.

cosmologists have calculated what the temperature must have beefing the

Universe was very small just a sort time after it came into existence.

the universe has a current "average temperature' of about 4 Deg absolute as measured by microwave background radiation. the intense energy "cooled " as the universe expanded.

at temperature an energy rises it becomes impossible for atoms to remain stable and the universe was a "soup of radiation"

when calculation are carried to extreme strange things happen.

We THINK we understand but there is a lot to learn.

Absolute Maximum Temperature

There is some question of whether there is a minimum... Much of that question starts with whether something at absolute zero would have no energy...

The thing is, temperature is something that we use in a relative way. absolute zero is just a starting point, rather like using the Big Bang as the starting point for time -- we have no way of measuring what's on "the other side"

I don't know the answer, but that is a really good question. I agree that there must be an absolute maximum temperature. Maybe it is inside a black hole?

Yes