You know, I saw this thread the other day and was going to comment that evenings/early mornings are fine but decided not to because I am in Texas (hot all the freakin time) and you are in DC (weather is probably very out of the ordinary for you). So I figured between the differences in environment etc my OTTB is probably more used to the heat than yours etc.
I rode her last night at 7:30pm, it was about 90-95 and not too humid. But the lil girl was lethargic, un-inspired and generally a bit laclustre which is quite out of character for her. So we just did an fairly easy workout and left it at that. She does better in the mornings, I think the heat of the day really takes its toll on her.
So my point is, listen to your horse and maybe try a morning workout if possible?
All horses deserve, at least once in their lives, to be loved by a little girl.