I cannot begin to offer any suggestions. When such things happen to me I contact local professionals. I sincerely hope someone here can be much more helpful.

They are helpful.

Either Ace or True Value are the go to places. Alternatively take a look for the model number online. You may very well be able to find a repair video or a parts list.

But, not having seen the controls or the heater, I can't guarantee that.

First, see if you can pull off the knob and see if the plastic ribbing inside is stripped. If it is and you can still turn the metal stub by hand, and it works, just get to a hardware store and buy a new knob.

If, however, that metal stub slips around not doing anything, or is stuck, you probably have to replace the whole assembly. Or more.

Usually, there are relays and resistors built into these things, and some even have proprietary chips and software. (I once tried to fix a vacuum cleaner that had a "digital control module" instead of a simple on/off switch. Yikes!)

At this point, you might want to get in touch with the manufacturer for help. And you might end up calling an electrician or recommended repair guy to do the job. And don't be surprised if just installing a new one makes more sense than fixing the old one. A new one might be similar labor cost, and have a warranty and be more electrically efficient than the old one.

As long as the breaker is off, you won't get electrocuted playing around with the thing. But, any time you play with electricity you have the (admittedly small) chance of fire when you turn the breaker back on.

Good luck.

I will take off the cover and see if it's just the knob stripped or the stub is worn. The fact that we have been having trouble getting it to turn OFF means it's had some extraordinary stress on it, most likely.

All good suggestions, thanks.

Most likely need to replace that. It usually requires some soldering, but you might luck out and it uses spade terminals, which is much easier.
Just like replacing a control on an oven or stovetop.

Oh lordy. Above my pay grade. Hahah.

Thanks for the reply. Appreciate the caution.