Question

Why doesn't the LED bulb heat up the room

Answer 1

LED bulbs do indeed generate heat as does anything that consumes electricity. The important thing to keep in mind is that LEDs consume a lot less energy than incandescent or halogen bulbs and are much more efficient in how they use that energy versus traditional bulb types.

Thus while LEDs will generate heat, it will be a fraction of that compared to a traditional technology bulb.