... but yeah, it'll be just fine. basically any card that has HDMI output should be totally fine. a $35 card like a GT610 / HD5000-series would be perfectly suitable. they're not very expensive (used on eBay is even cheaper), many are in a slim or low-profile format, none need any extra power, and a bunch of them don't use a fan but just a bigger heatsink to stay totally silent.