First question would be whether you have measured the effective rolling diameter of the inner (Goodyear) vs outer (Bridgestone). If the inner tire is larger, therefore carrying more of the load it will be warmer.
Also, inner tires, because of less air circulation DO run warmer than outers.
The answer as to "how hot" they can get-- tire engineers I have read suggest this is really not an issue-- even 140 not being excessive. Sure, will accelerate wear, but not dangerous. Their basic answer is to run the correct PSI (checked cold) and don't worry about temperature.