As I was thinking later about the closed top, it dawned on me that if you used the airpump to replenish the oxygen depleted by the higher temp, you would be putting the air in the tank so sealing the top probably wouldn't matter.
I know lots of people claim running an airpump helps cycle faster. I assumed this was because of increased dissolved gases, but who knows, it may help bring more "seeding" bacteria into the tank.