I'm so sorry to hear about your son and grandson. That has to be so hard for you. That heat sounds awful though.

This is just a thought...
Could you go for an inning or wait in air conditioning until it was his bat a couple times? I've no idea if that would be practical given driving time, but something to consider. Hopefully, the weather for the next game will be cooler..

My grandchildren are young, but have started swim teams. Summer here is ok with meets being outside, but I've debated like you about indoor meets. I went to part of them last year and if the pool area had a lot of humidity (a couple really did), I'd go out in hall or outside until my daughter messaged me that his event was approaching. She also sent videos of his laps and I'd send him a note for a couple I missed. Perhaps his mom or another relative could do that for you.