Are you sure it's heat? Heat could be the culprit, but unless you're regularly running hot (think 90C+), it's probably not heat. Even 75°C would be normal for a graphics card, and "feeling a lot of heat" and hearing your fans when playing something graphically intensive would be expected at those temps.
Three common causes of crashing that aren't heat-related:
- Bad/corrupted driver
- RAM going bad
- PSU going bad
Try a fresh driver install. How old is your RAM or PSU? Try playing games with your RAM set at JDEC speeds (turn off XMP). Have you checked for BIOS updates?
If you're thinking it's heat: when was the last time you changed the thermal paste on your GPU?
For your second question, I'm not actually sure, but I would think that a more powerful card should produce less heat overall for the same workload (in general), since the equivalent processing power of older hardware has ideally been crammed into a smaller footprint.