WOW! A good catch; a pair of swim shorts is a cheap price to pay, considering the altenative. I changed out all of my interior DC lights with LEDs right after we bought the PC. I removed the lights, replaced the (ugly) flourescent tubes with strips of 3528 LED strips. I just bought a 10' roll and used the adhesive strip to attach them. A mistake; the adhesive strip doesn't last long, so I eventually needed to apply glue to restick the strips to the roof side of the light. By doing so, I could control the brightness of each light fixture, by the length of strip that I attached. In my 2011, the lights had a three way switch, low, high & off. I cut long strips for a "Coach Cleaning Mode" - SUPER bright and a shorter length for low lumen use. Except for the adhesive facet, I have been very happy with my conversion. About an hour per unit time for the change out, including the removal, disassembly, reassembly, glue dry and reinstall.
Incandescant bulbs dissipate somewhere around 80% of their energy in heat. Good for you for catching this, before it turned tragic.