Yeah and warming up my eye/brain isn’t a pretty thought. Head impacts brain function, and the last thing I want is a part of my brain getting more sustained heat than the rest.

I think you vastly overestimate how much heating is at play here. Think of how long it takes a 1000W microwave to heat up a cup of water, maybe 2 minutes. Now imagine one tenth of that, or even less, even if it's microwave radiation you might never even make it above lukewarm. Blood is fairly good at taking heat away, just about as good as it is at warming you back up from the cold.