We installed a Panasonic fan that has light, heat and night light. I'm not sure if the main light is an LED. Panasonic fans get good reviews.

Sure, Build.com and other sites sell them. Found one in about two minutes. Here But they are not going to work for a sloped ceiling. No one probably makes one that swivels like you would need for that application. Heat in a radiant form, as in a light bulb heater, travels in a straight line and you will be heating whatever surface the ceiling pitch has the bulb pointing at. You need to build out a triangular box to put the fixture in. You can drywall it so that it is not as obvious as mine was. It is not a great picture, but in the upper left side of the photo you can see the maple triangular box that gives my light fixture a level surface to hang on.

Teacats, love that bathroom! I wish I had a bathroom w/ a vanity large enough to do something like that. I'm glad to see this question raised because I just put a small lamp on my kitchen counter and have a lot of extra cord. Unfortunately, I can't tie up the whole cord because it has the on/off switch *on* the cord (hate that...). But I can tie up most of it and attach it somehow under the upper cabinet.

The Panasonic unit has a heating element, not a bulb. Something to keep in mind with the coming restrictions on incandescent bulbs, though, so far, infrared bulbs used for heating are not included--in the US, at least.