Actually the idea is to run a vacuum in the crank case. This allows the rings to seal better which helps keep the vapors cleaner. The pistons have to push less air if you maintain a vacuum in the crankcase and a good deal of HP is lost in pumping air in and out of an open breather system. So much that the pros run a extra pump just to pull a vacuum in the crankcase. The air oil separator a large one not the poopy little cans you see for sale allows any oil vapor to drop out of suspension so only clean air enters the intake and the amount of heat is negligible compared to the amount of cool air the engine takes in .
I have seen the effect of this on Ducati bikes on the dyno. Now I'll grant you that the Ducati twin is particularly susceptible to this because the pistons actually both go in the same direction during parts of their stroke so they displace a lot of air. But when people remove the check valve and run a K&N filter on the crankcase breather they loose hp. They gain hp by running the check valve and then into the air box where there is a slight vacuum.