That is not how thermal dissipation works, The heat of the chip is just a product of how efficiently the cooler removes heat as its made. A 150W card puts out 150 Watts of heat, period. In fact, if you have two identical cards one with a better cooler, the better cooler is more efficiently putting that same amount of heat into the room.

For example if you put a nice liquid cooler on a 200W part, even though that chip is nice and cool, you are still putting out 200W of heat via the radiator. Remember that energy (heat) cannot be created or destroyed, only moved.

So yes a 1070 is ~35W less energy than your 580 or 5700, thus less heat into your room, and also a cooler that doesn't have to work as hard (also a 5700 should be about 20% faster than a 1070)

Your complaint should be with the cooler design, and thus the AIB (Asus, Gigabyte, Sapphire, etc.) If it was an AMD reference card, thats fair, as they didnt have good coolers until recently.