Did your new master cylinder have a metal rod that fit in the master cylinder between the booster and master cylinder? If so, I have found these to be a hair too long, essentially pre-loading the brakes. What makes it worse is that every time you press the brakes the master cylinder is not fully returning to the resting position so it’s constantly retaining more pressure. The heating up and expanding of everything under the hood doesn't help either. To test this, drive the car and get it hot like you described and immediately (once home) back off the two nuts that secure the master cylinder to the booster jack up the front of the car and spin the a wheel. If the brakes loosen up you found your problem. If so just grind a little, like .050 to .075, off the rod to gain a little clearance.