|No, but you will suffocate.|
What do you mean by no air in the room. The only place you are going to get that is in a vacuum chamber.
If the fans and heat-sinks are correctly fitted the air will circulate and that will keep it cool.
If there is enough air in the room and enough ventilation to keep you alive then there will be enough air to keep the CPU cool.
However, if you are planning to run a PC in vacuum chamber then it will burn without some cooling. In that case you will need water cooling.