i have been reading the barker's book and they said to check on eggs every couple days and to inspect the bottom of the eggs for mould if the egg box doesnt smell fresh. they have room incubators so removing the eggs from the egg boxes will not result in too big a change in temp for the eggs. so i guess its not a big risk for them.
but in my situation, whether you are taking them out to inspect them or just checking up on them could the drop in temperature or the draft of room temperature air damage the eggs in anyway?