Absolutely. Using a dry side towel might be iffy sometimes, but the wet one in those situations will burn you.
Burns are painful, but stream burns are the worst.
Q
Yes, so many calories of heat in steam! You raise an interesting question: Do you think a “wet towel” burn is because of steam or just conductivity increases by virtue of moisture?
Kevlar mitts for seriously big or unwieldy stuff. I really don’t like silicone mitts or potholders. I have really old and ratty quilted potholders for small stuff. My Kevlar mitts are not the puppet handed ones I tried puppet mitts and couldn’t get a grip on anything.
Sometimes, I’ll use a folded kitchen towel. … a dry one, of course.
Ahh, for those good old days in college with asbestos mitts and ironing board covers … what we didn’t know. 
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I use a quilted mitt, or square quilted/terry type, or a bar towel.
depends on the task!
I have however stopped using wet/damp towels - after a couple really nasty burns when the (cast iron) handle steamed through the towel . . .
