yup. That would probably do it. You might have to tweak the PWM circuit a little to get a more reasonable frequency on it if it's unsuitable as-is, but that would be as simple as probably just swapping out one of the capacitors on the board.
You will also want a switch in there so that you can manually shut the element off, but you should be able to get such a switch at the hardware store for (guessing) $5.
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