Hoekie is certainly correct about the expansion/contraction of the metal... a 3-inch razor blade will expand about 1 one-thousandths of an inch for a 20-degC raise in temp. The expansion/contraction is linear unless there are stresses in the metal (and there almost always are) in which case there will be deformities (curling, buckling, etc.).
It's hard to imagine there is much effect on a razor's edge... but a while back I began to think my razor got dull when I rinsed it in hot water while shaving so I started wiping the lather off with my finger and flicking it in the sink. I never thought much more about it... but now that I do, I'm guessing there could be significant stresses built up in the edge due to the rapid increase in temperature induced by rinsing in HOT water which would warm the edge faster than the thicker part of the blade. :confused: And, it makes my head hurt thinking about it.
As an aside... In another life I did some computer automation of the machine shops for a manufacturer of military equipment. The shops were not air conditioned -- in the winter it was cool and in the summers warm (say a range of 50 to 100-degF). Because of the close tolerances needed, they had different programs for (as nearly as I can remember) each 10-degF temperature change. Some of the parts were produced on a 90-foot long milling machine made, predominantly, of cast iron. The parts being produced were titanium, which has a much different coefficient of expansion than iron. Thus, for a given temperature change, the machine would expand/shrink a different amount than the part being made -- hence, the need to adjust dimensions.