You’ve got it backwards. Warmth makes it expand, cold makes it contract.Eggs that need to be washed should be washed in water at least 20 degrees warmer than the egg itself. This causes the egg to contract, pushing dirt up and out.
Washing in cool or cold water will cause the egg to expand, sucking the dirt and bacteria into the interior of the egg.
There's lots of university and other sites that explain this, here's one:
http://www.ianrpubs.unl.edu/epublic/pages/publicationD.jsp?publicationId=798
