Hi jknight. Good question! Absolute zero is easy, because it is just particles with no kinetic energy at all. But what does it mean to have “absolute energy”? The Standard Model of physics, which is the current reigning champion and the one on which most big-bang ideas are based, has a value called the Planck temperature. It is 10 with 32 zeros after it, which is inconceivably hot. The only time it would have been reached is just after the big bang. It is a limit, because space-time sort of breaks down after that point.
String theory generally predicts a maximum a fair bit colder than the Planck temperature – although by “a fair bit”, I just mean you can knock 2 zeros off that very big number.
Hi jknight! If I had to choose I would side with Drew. The Planck temperature is certainly the hottest of the hot as far as fundamental physics is concerned! Anything hotter is meaningless. However, as Drew nicely pointed out, a absolute maximum temperature isn’t well defined. Definitely not in the sense that a minimum temperature is. I found this article interesting on contenders for what the hottest possible temperature is: http://www.pbs.org/wgbh/nova/physics/absolute-hot.html
Clearly it is still a matter of debate!! Great question!