i've read the reasoning behind that recommendation and while it sounds good in theory, it really doesn't follow logic. cold is the absence of heat and heat will migrate. using a water that is hotter then the egg will cause the cooler internals of the egg to want to draw that heat and whatever else you're trying to keep out of the egg inward, and would not push outward. washing in a water colder then the egg would cause the reverse of that.
I think you are in error here.
Think of the egg as being Neutral Temp.
If you dunk the egg in cold the egg interior will shrink drawing air and contaminants through the shell. The air sac will shrink and pull "stuff/germs through the shell. The shell is porous.
If the water is warmer than the egg it will cause the contents of the egg to expand and nothing will go into the shell until after it is disinfected. When it cools from disinfecting it might pull something through the shell, but everything is sterile then.
You have to remember we are dealing with rules for gas and liquid not solid. A solid would expand as it cooled. Egg interiors are liquid.
Far greater minds than mine have explored this, anything you read on the subject whether eating or hatching eggs says water warmed than the egg.
Now there is not going to be much expansion as the eggs is not in the solution long or under the facet long, it is never going to warm enough to kill the embryo. It would only take a minute amount of contracting to pull a bad germ through the egg contaminating the egg and the incubator.
I am thinking of taking a hatching break to re-sterilize my incubator. or maybe move the eggs to the hatchers for a day while I we-sterilize.
I am actually worried I might have brought something into the incubator before I did the disinfecting of the eggs...
I also know most people here say not to disinfect because of the bloom. I am going with the experts until proven wrong.