Molecules will break apart above a few thousand degrees. If you take a gas (say Helium) above a certain temperature (probably ~1e4 K) the collisions between the atoms will knock the electrons off and you'll be left with a plasma.
Confining a plasma could either be done with magnets (e.g. a fusion reactor), or with more plasma! (in the case of stars, where the gravity keeps itself from exploding).
Above 1e7 K you start to get fusion of Hydrogen, and I think above 1e11 K pretty much any nucleus will fuse/break down.
So it's difficult to say there's a maximum temperature, as it's quite hard to define.
What's your maximum temperature? About 41'C... above that and you'll die...
Hopefully there is some clarification to explain how I won't die...
BTW, as a teen I remember playing out in the sun at a good 52°C. Don't think I died :)
And yes, these are well above biologically-friendly temperatures. :)