All the people saying to use x thing. This is clearly in a hotel room, otherwise OP would have had other options.
And OP? You monster! The next person to use that iron is bound to be some broke graduate, who have spent their last money traveling for a job interview, and now you've destroyed their only decent button down shirt.
Just use tools that are made for food. Put a pan on the stove and use it like a hot plate. Heat upsidedown, but not till the cheese melts, then flip and heat from the base.
American cuisine
https://en.m.wikipedia.org/wiki/Dishwasher_salmon
Lol I hope that's not a thing fr