I have also had my share of adverse condition gigs.
I have done an indoor gig at a club some years ago that all the guys in the band spend half naked in the dressing room because it was too hot( around 110 degrees if the fahrenheit converter is right). There was no A/C and not that good ventilation. We still went for it, 30 minutes later passed out. I got a bottle water shower, took my shirt off and finished the gig. We didn't get paid.

Not looking forward doing that again any time soon.
2 years ago the band I was playing with got a beach bar gig.(Dream gig I know right? NOT!) We were scheduled to play there every weekend. First weekend= Hell.
Sunburns, heat exhaustion noticeable crotch sweating. Second week=Epic. Put on a cool hat, sunglasses, tons of sunscreen, lots of water, swimsuit and flip-flops. Cool like a cucumber and we played all the way till it was dark.
And last but not least last year I moved to Germany and I played a gig in a wonderful club without any heating(it broke down and the place is basement) in the middle of the winter which means 5 degrees.The owner told us it is ok if we want to cancel it but the other people in the band thought that once room is full the body heat of the crowd and lights will help. Well, they were wrong. My hands were blue because I didn't have any (emo) gloves, I played while wearing a jacket and a isothermal beanie. To our luck we used the hand dryer on the bathroom which really helped.
All said, I have to admit that you should draw a line on conditions. However, if you are young and stupid and/or have a good health insurance go after it no matter the conditions.