If the energy density in a fixed volume of space gets too high it collapses into a black hole. That seems to suggest that there is a kind of limit to temperature.
Only if it's concentrated. Otherwise the entire universe would have collapsed into blackholes during the big bang. You need an energy gradient for gravity to work like that.
I'm a complete noob in this area, but that doesn't mean that temperature has reached it's limit does it? The black hole can carry on getting more dense and hotter.
No, the black hole can't get more dense. If you put more energy into it it gets bigger.
Schwartzchild radius is directly proportional to mass, so (if I understand correctly) it's if the energy density of a surface area rather than of a volume is too high.