If there was a perfect environment, and something was able to continue to heat up indefinitely, what would happen?.. What would be the outcome of something continuously heating up?
No. At some point the kinetic energy of the sub-atomic particles making up the object will be greater than the binding energy of those particles. This may be a very high temperature for particles bound with the strong (or weak) force.
In practice, the atoms will fly apart when the kinetic energy is great enough to overcome the attraction between atoms that holds the molecules together. The particles move away from each other so fast that they cannot exchange kinetic energy by collisions. This is one problem with trying to build a fusion reactor; the hot particles keep escaping. (Stars avoid this problem by being really big.)