Our first two years here were 110 heat waves and humidity is always high here.
High tunnel won't help that anymore than shade cloth, aside from the occasional splitting rain no longer being a thing. It's a watering control and also season extender. I'll be able to start a month earlier and end a month later on many things and grow a few right through winter.
I do the same. My greenhouse is unheated. Gives a jump on the season and extends it on the other end. Plus, it’s my She Shed and makes me SMILE whenever I am in it. :)
My best? Ripe tomatoes at Christmastime. But, that has only happened ONCE so far in a very MILD winter. ;)