I know there is a theoretical minimum possible temperature but is there a theoretical maximum possible temperature as well?

At what tempurature does matter and energy become the same thing... and what pressure is necessary to maintain that pressure?

A black hole comes to mind for me but I don't have any idea how one whould measure such a thing.

To heat a system, energy would have to be transferred from another system. I think there should be a limit to how much energy that system can transfer to the system being heated, considering the amount of mass it contains is finite. We cannot consider an open system to heat another system because of the heterogeneity.

There is the Hagedorn temperature for systems in which the entropy is proportional to the energy. This gives a maximum temperature, that is you can increase the energy but keep the system at a constant temperature, this the Hagedorn temperature.

 

This idea comes up in string theory, the theory of quark-gluon plasmas and I am sure other systems of physical interest.