we moved into our current house a few years ago, which is all electric.
When we moved in, the heat in one of the bedrooms didn't work.
Luckily there was a company nearby that had a specialist for ceiling
heat. Even for him it was tough finding the break in the wire (without
otherwise damaging ceiling plaster everywhere).

I live by the phrase "if it doesn't stink, don't stir it". Our living
room doesn't have a fixture in the center of the ceiling. All of the
other rooms do. Although it'd be nice to have a ceiling fixture in the
living room, I don't want to screw up the heat, so we use a switched
wall socket and table lamps.

If you do decide to try your lamp, check to see in advance that you
have an electrician who is experienced in ceiling heat issues.