I did a little research, but couldn’t exactly find an answer: Is there a defined physical limit to how hot something can get? How big? How dense?
I’m assuming that if an object gets hot enough (say, the core of a star), it’s a physics impossibility for it to get any hotter. Am I wrong?
Thanks,
Adam
Density is likely limited by a mass’s Schwartzschild radius, the radius of the sphere to which if the mass is compressed it will form a black hole. For a time physicists did not believe matter could be compressed this close; the supposed compression limit was observed in the neutron star, where matter’s atomic structure would break down, leaving only amorphous elementary particles (essentially the density of an atomic nucleus). But obviously the confirmed existence of black holes shows it can be compressed further.
I would assume a heat limit (temperature increases with compression) would also be imposed by spacetime-curvature, though I don’t know for sure.
I could make a quip about how some posts on the SDMB prove that there really is no limit to density, but I’ll defer to the better angels of my nature 
The basic answer is “No”. However, the universe does place restrictions on what matter can do in a particular state. For example, matter above a certain density can only be part of a black hole. There are also extremes where the currently-accepted equations of quantum physics break down, but that’s just a limitation on our scientific knowledge, not on the universe itself.
DISCLAIMER - I Am Not A Physicist.
What does hot mean?
The relationships among heat, temperature and kinetic energy are by no means simple. Do a search on “negative temperature” here in GQ and you’ll have lots of reading material.
Note that the density of a black hole depends on the size of the hole. A stellar-mass black hole will be denser than anything else known, but a supermassive black hole such as are found in the cores of galaxies can have a density comparable to that of water, or even air. And a black hole of less than stellar mass, if one could somehow produce one, would have a higher density even than a stellar one. The smaller one makes a black hole, the denser it becomes, with no known limit (though there may well be an unknown limit; a reasonable guess would be around 5*10[sup]93[/sup] grams per cubic centimeter).