It's doesn't get super humid here like it does there, but I've found that my mare does well getting a tablespoon+ of loose table salt in her "grain" twice a day on hot days (encourages drinking and helps balance what's lost through sweat) as well as once/twice daily hosing (on super hot days I'll hose her off in the morning and in the evening but usually I just hose her in the evening).
She's a bit different than your guy though. Her "issue" is that she's 28 and will stand in the direct sun alllll day unless I lock her in (which is another thing I do on super super hot days, for her own safety). Anyway, if I just let her be and don't hose her off, she starts acting "kooky." "Too-hot Lacey" is pretty cranky, slow to respond and will often act sort of lost in areas she's totally familiar with, where she's usually a pretty sensitive mare.
Anyway, basically I know how she acts when she's too hot and as soon as I see those signs, I make sure she gets cool.
Try the salt in his feed, that has seemed to really help Lacey. You might start with 3T/day, or more. 4T is my usual "dang, today is HOT and the old girl is sweating super bad" go-to. She just loves her salt! Haha
Fabio - 13 year old Arab/QH gelding
Hazel - 14 year old Angora goat
Atticus - 4 year old LaMancha/Alpine cross goat
Rest peacefully, Lacey.