You may want to check the new publications of Prof. Miroslav Grmela in our department, he recently started working on modeling of thermal properties of polymer nanocomposites:
There is nothing you can do about thermal conductivity, as it is governed by electron transfer which is not the topic of MD at all. Also for thermal stability if some sort of reaction is involved (like oxidization) you are going to need a reactive force field which is not highly accurate. But if your are looking for physical instability (or bond dissociation) just by replacing harmonic bonds with well optimized Morse potential, you may get some insight on your system.