The comparison is perfect.
Why would someone heat balls in 10 degree weather? Because when it is that cold outside, a heated ball would be easier to grip, handle, throw and catch. (Yes you would increase the PSI a bit, but softening the ball with warmth would more than offset that.)
Why would someone deflate balls in 45 degree weather? Because it would make the ball easier to grip, handle, throw and catch.
The crimes are identical because it is tampering with equipment. The motive is identical because it makes the ball easier to handle. The only actual difference is the Panthers were caught red handed on live TV, whereas the Patriots were completely innocent and the whole accusation was complete and total bull****.
Not necessarily "perfect" as we both agree that, if the goal is to lower the PSI, then heating the balls on a cold day would do exactly the opposite.
That being said, I don't know for sure HOW the air inside of the football would react compared to the texture of the pigskin.
In fact, what would be interesting to find out - and any University science student could probably figure this out - is the question of how long the desired effect of a heated pigskin itself lasts, compared to the temperature of the air inside
That is, it MAY be that the softer, heated pigskin retains that quality long after the temperature of the air inside - and thus the PSI - reverts to the natural conditions.
Air and Pigskin are NOT going to necessarilly react as quickly to the same conditions - and I'd say it's plausible that pigskin itself will retain heat longer than the air inside
Which means, while the comparison is far from perfect, the notion of heating up footballs on the sidelines COULD be found to soften the outside, while the inside quickly reverts to the colder, lower PSI
In other words, it's possible that heating the footballs on the sidelines could be "worse" than what a few remaining delusional fans insist is what the Patriots did (despite the PSI itself proving no tampering occurred.
Now you have me wondering! Might be worth posing that question out on Twitter for any of the entities that replicated the PSI of the Patriots footballs from that day in 2015!