When Frasier takes the game hens out of the oven in his apartment one one side of the pan his hand is on it without an oven mitt or towel so it's unlikely that his hands would not get burned a little.
When Niles and Frasier are fighting about the sauce you can see that as they are both holding the pan at the bottom. How could it not burn their hands if it had just been taken off the stove?
Worker: Excuse me, it's after four o'clock, what if I finish this tomorrow?
Niles: I suppose -
Daphne: Oh no you don't. You said one day when I hired you and that's what it's gonna be. So get cracking cause something's gonna be hanging from that rafter by the end of the day.
Roz: I can't believe you're so calm. I'd be a wreck by now.
Daphne: Well, I was nervous at first. But at every step I thought, "How would Frasier and Niles do this?" And I didn't do that.