You can do ironed cheese sandwiches,* so they get plenty hot, but most modern irons will turn themselves off if they’re not moving for more than a minute.

*Assemble the sandwich on top of a generous piece of aluminum foil, heavy duty if you have it: butter on the outside, cheese on the inside, sourdough with cheddar is excellent but white bread with American is what the kids expect. (Don’t get too creative with additions until you have a good sense of how long to melt the middle without burning the outside.) Bring up two foil edges and fold that seam at least twice, making it flat as possible against the sandwich and able to channel any escaping butter towards the ends rather than just seeping down onto the ironing board. Then fold the ends as well. Maybe you better put a second piece of foil on your ironing board just in case. Put the iron on top heat but turn off the steam. Iron the sandwich on both sides, starting with the seam side and then doing the bottom, until it smells toasty and delicious. Only move the iron enough to hit all the corners and also keep it from turning off, and don’t press hard.

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Probably, it’s probably quite inefficient though.