What condition is the mirror glass? Does it have any imperfections? I've had the heating elements in my e34, e38, & e39 side mirrors fail...which only required the purchase of new mirror glass to "fix" the issue.
If you only have the heated side mirrors...they probably aren't that expensive...if you have the heated/EC (auto dimming) side view mirrors...then be prepared to shell out a few Benjamins.
If the wiring all the way up to the mirror glass shows voltage, then the issue is probably with the heating elements of the mirror glass.