Of course! Lol, if you didnt reinstall your OS than you should probably ignore my post and do that first.
As for the heat, the cpu without heatsink(and thermal protection) would go up in smoke in seconds, so if the heatsink isnt touching properly it will take slightly longer depending on contact between cpu and heatsink.
No, I did not re-install the OS (yet), but I did re-install the heat sink with new thermal paste, and, low and behold, the machine kept running!!