I’m not in any way a builder/bodger, but having just had to patch a ceiling, its not actually that hard.
You cut out the damaged piece of plasterboard, and enlarge in rectangle shape to nearest wooden beams behind. Attach new strips of 2×2 to the inside edges of current beams to screw replacement board to.
I guess at this stage you might also consider putting additional wooden beams in as attachment points for your heater?
This is the easy bit – if I can do it, anyone can.
Then follow one of many youtube videos for plastering a patch, which they make look easy, but is not so much….