No. I used to do it, but it lengthens the incubation time. I did a trial, one batch of rouens cooled and one not. The cooled ones hatched a day late, but other than that they were ok. One was assisted due to a malposition. One died before it pipped, not sure why. I got 100% hatch rate on the uncooled batch. They all hatched overnight on day 27. That confirmed my suspicion it's unnecessary. This was also a relief because there are little kids in the house and I have to take all of the eggs out of the incubator and lay them on a towel to cool. I never cool now, and my hatch rates are just fine. You can if you want to, but in my experience it doesn't have any obvious benefits. I do mist the eggs after each candling, because they cool a bit while i candle them.