What theories exist connecting volcano temperatures to eruption probabilities?
I have not heard of complete theories connecting volcano temperatures to eruption possibilities either. If you mean subsurface magma temperatures, it is uncommon for there to be direct observations / readings for a particular volcano. Fumarolic temperatures, on the other hand, are directly indicative of current volcanic activity and are much more easily measured (example). In addition, geochemical analysis of fumarolic gases can be related to eruption probability (example, example).

Even in models of magma ascent, temperature differences are not the main focus, but rather pressure differences are (example). This is directly related to g.z.'s comment that volatile content certainly can be a dominant eruptive trigger.