When using an SLR that has the live image feature available and enabled how damaging is it to the sensor if utilizing this feature causes the sensor to heat up? Are there some models that do not have that disadvantage? What is the best SLR available for under 1,500 that has the live image option feature? The camera would also have to have a port for a corded shutter release. I need these features for a very specific application.

40D is the only Canon camera in the price range with that feature.

On a CMOS, I don't believe live image would be a problem with heat, because of the way the CMOS work.

I assume you're using it for Astro-photography? Generally the only people really worried about it overheating as astrophotographers who capture images for hours on end at a time.

Well, I haven't seen it happen with my 40D yet, but there is an error message that will warn you when the sensor temp is too high.

It doesn't seem to be a huge problem, even after a couple of hours. Check out this quick test - not as definitive as one would like but encouraging in terms of noise under fairly extreme conditions!