Last night we watched a full HD movie and were in for an unpleasant surprise. Just when the movie was about to end, the computer turned itself right off. I suspected overheating so I checked the temperature readings in BIOS and they were extremely high (79C)! To solve the problem I temporarily mounted a slim 60mm AMD stock fan above the heatsink. Since it doesn't cover the whole heatsink, a real solution would be getting a slim 100mm fan which I'm going to have to order from the UK.
Conclusion: The board obviously cannot rely solely on passive cooling, at least not in a slim desktop case. You will have to provide for adequate ventilation or face potential problems with overheating.