I've done the heat thing to free stuck nuts and bolts many times.
One technique that I've used when I'm concerned about damaging the surrounding area is to use a soldering pencil. Plug it in, heat it up and prop it up on a piece of wood so that the tip is resting on the screw but the rest of the pencil is safely away. Let it sit for 15 minutes, take it away and melt an ice cube on the screw.
It may take a while for the screw to absorb enough heat, but I've never damaged the surrounding area