Again it's a software trick to show "corrected" altitude as if you calibrated manually every X minutes, it's not magic, they have nothing more to work with than the GPS altitude and the barometer.
Heating the watch probably affects the operation of the sensor itself rather than the air around it.
I explained above why you'd want to display both at the same time, that shouldn't be too difficult to "GET" either surely ?
GPS altitude IS correct, barring any catastrophic environments, the only problem is that it changes a lot so messes up D+/D-, hence the inclusion of barometer sensors on GPS watches, and of course they're useful to anticipate/understand trends in the weather.