I'd say that depends on the dimmer. If it can get a lightbulb down to being off, then it should be able to do the same with a UTH. I'm using one right now (we have a thermostat we'll probably hook up this weekend, but just haven't wanted to bother her with it yet...) and it works just fine. The one I have has a little slider thing which includes an off setting
http://www.homedepot.com/webapp/wcs/...ctId=100145680