Does a lower profile tire with less air volume generate more heat?
Most heat is generated by the flexing of the tire carcass. A softer carcass, either by design or due to lower inflation, will create more heat (all else being equal). I didn't realize that TPMS gave you a temperature readout, but if you're using temperature to compare the Avons to the Bridgestones, I'd suggest the Bridgestones are a softer (more flexible) carcass.