Fresh eggs do need to be refridgerated like any other eggs, especially if they are fertile.
They should be washed in 120 degree water with a splash of chlorine solution (or dish washer det) gently scrub off poopy/straw/mud and immerse for 30 seconds, immerse again in 120 degree rinse water & drain, wipe dry, and refridgerate.
here is a good pulication from U of NE:
http://www.ianrpubs.unl.edu/pages/publicationD.jsp?publicationId=798#target
The ideal water to clean eggs should be at least 10 degrees warmer than the eggs are, up to 120 degrees, as the egg is 110 when it comes out of the hen....believe it or not.
Edited to add:
The only eggs we do not wash & refridgerate are hatching eggs, which any light soil is sanded off with a 3-M pad, and eggs stored at 55 degrees and rotated several times a day, to keep the embryos dormant.
Any warmer & bacteria and the embryos will grow, the embryos will then suffer at any temps under 99.6 and give up in early stages of incubation, making what is called a "blood ring"
hatching eggs must be kept under 60 degrees, chilled, but no lower than 50 degrees.
Alot of folks think hatching eggs must be kept warm and that is far from truth, they need to be kept cool, until warmed to room temperature before setting under a broody or in an incubator.