If your case is ATX standard, it should fit. It's a large card, and yes it's a bit of a squeeze... I was wondering the same thing with my gtx680... it has about 3mm room at the end and I had to relay some HDD cables for it.
The case you linked appears to be an ATX standard Midi tower. I have the same size case. If you want to make sure, contact the supplier, he should be able to tell you a yes or no.
Heat is a problem in small cases (same boat here) and on hot summer days I have to remove a side panel because of it... but mind you - my system and especially my card are heavily overclocked, so by default I have much more heat buildup. You should not have that problem if you don't overclock the card too high (or at all). My ambient room temp. is 30-32 C here in summer, so it's pretty hot here compared to other parts of the world. The card itself is thermal protected, meaning that if it gets too hot - it will downclock itself to cool off, so it wont burn down everything.
As Raynard says... open your case and check the power supply (PSU)... you need a minimum of those requirements to run that card (good point... I forgot that :\) 550W being the bare minimum, It's better if you have some headroom, say an additional 50W, for the sake of stability.