For what it worth my car was painted in the middle of the summer in AZ. It was in a booth, but it was not cooled in any way. The booth had the floor soaked, so I am sure the humidity in the booth was up there some as well. I am not a painter but I do know this is why several different hardeners (?) are available, you use a certain one based on temps from what I remember.
My car took a while to get painted, but then again EZ works a regular full time job and does body/paint on the side so it was to be expected. Really hope you do not get screwed over.....