You already bathed him and things went well
I was going to say it depends on the horse.
I have one out of four horses that is "hot" enough to tolerate a bath in the conditions you mention, and I have bathed him in that kind of temp without issues.
Two other horses will easily tolerate a full sun bath when the temps hit the mid-70's.
The fourth, my Arab, needs to not only be in the full sun but he thinks the temps need to be a minimum of 85 degrees
He just turned 27 so I try to be sympathetic
I need somebody to video the contortions he goes thru when the water hose hits him even at 80 degrees. And I use the soft spray on shower nozzle dial.
It's got to be around 95 degrees for him to actually enjoy getting a bath.
So ---- it depends on the horse