I have two 770 4GB cards. First I went to a 4k monitor with the single 770 card. For the desktop (win7) and civ it was no problem civ runs maxed out and the card runs quite cool. I put in the second card for more demanding things and wow civ5 starts running really really hot, I was surprised. Fortunately Nvidia lets you turn of dual cards for things like Civ5 that don't need it and it was back to normal coolness...I have an old very large dual xeon case so two huge cards in of them selves don't block air cooling, it's something about having both cards on and working that magnifies heat way more than the double heat I was expecting.
Now I'm running 4kat60hz using display port and I hadn't thought about limiting it down to say 30 for things that don't need it but really my 770 card when alone is very cool running (way cooler than my old 550 card ever did). I've never burned out a graphics card yet and I started using them when they first came out, but they always become obsolete before they burn out (and I tend to build my computers to last many years, the recent upgrade to 4k was due to an unexpected windfall).