If the person saying it WILL lead to video card burnout would like to explain what they mean then you might get a little more info. However IMHO it smells of horses**t.
Currently, my several-year-old HP Microserver with a passively-cooled video card hasn't burned itself out, and several thousand other people with similar kit running XBMC etc don't have the issue either.
Video decoding is not a high-powered requirement for video cards. Hence you can get away with a passively-cooled one rather than requiring a fan (and it's usually fan bearings giving way and the card cooking which does for video cards).
Please note, the decoding and display of MPEG-2 video is considerably less intensive than the *encoding* of such media, which is where SD is seeing his temperature spikes. You won't be encoding anything when watching tv.
As regards HDMI leads, there are different standards, however getting a 1.4 video lead would suit you as they're backwardly-compatible (and I doubt you're talking about 4k images over broadband
)