I only candle twice, at day 10 or 11 (depending on my work) and again at day eighteen. I don't worry about them getting cold as it only takes about three minutes per tray. I use a Sportsman and each tray holds two racks of eggs.
I just pull out the tray, set it on a desk beside the incubator and candle the eggs in the trays without taking each egg out. I pull out any that are not developing and put them in a waiting egg carton to dispose of later. I do shut the door on the incubator while I have the tray out. When I'm done, I re-insert the tray, kick the turner back on and go on my way. I always check the humidity pans every day, and if I need to add water I just have the water ready, open the door, pour in the water and shut the door. Takes maybe a minute tops. I've had as much as 100% hatches.
In nature the eggs get to cooled down a bit when the hen leaves the nest to eat and poop, so it's not going to hurt them.