As the expression implies, a very warm/hot place. This effectively communicates that it's uncomfortably hot, just as a whorehouse would be from the droves of people who would show up for "dollar night."
Sam: Why is it so warm in here. Dinner will cost us $100 each; you'd think they can affordair conditioning!
Nora: Yeah, it's hot as a whore house on dollar night.
Percy: "Man, look at these hands! They are calloused and bleeding from all of that yardwork!"
Samantha: " You let that shit get overgrown and it needed to be done. Stop acting like you're sore as a door on a whorehouse on a payday. Now fetch me some sweet tea!"