Yeah, welding in the summer kinda sucks. Especially TIG 'cause it requires a bit more comfort and concentration to get a good weld. And you can't have a fan on for air circulation 'cause that'll blow your gas away.
I usually use some lightweight coveralls, blue cotton Navy issue. Depending where you are, you can usually find these exact ones in thrift stores for cheap. Sometimes it's so uncomfortable though I just put a T shirt on and slather up with some 50 spf sun block. I get so lubed up I could probably do a slip 'n' slide on the garage floor!
A tip for the summertime: This pertains more to welding aluminum than steel but, it does happen with steel too. You may find after you've been welding a bit that your rod hand starts to get shocked. It's 'cause your hand is sweating and glove's getting wet. Use latex gloves under your welding gloves. No more shock.
-David