The blades are pretty crudely stamped, so the edge would expand ever so slightly in the heat, and ba 'blunter'.
I've looked at them under an electron microscope and they are actually very, very smooth. Agreed, the edge is actually quite "rough", but this is on a scale of microns!
It looks as though they are formed from strips of very carefully rolled steel strip, cut to length and then sharpened on some sort of abrasive strip - all the marks from sharpening run at right angles to the blade.
The edge is not thin enough to change shape noticeably from heating/contraction. Urban myth in my opinion, although of course you skin will respond drastically to hot/cold water - especially the orientation of the hairs.
As for razors, I like the simple Gilette twin blades without the lubrastrip. You can still buy the blades, but the razors are long gone now. I've tried the Quattro, the triple baldes, all the new fancy ones and none of them are as good as the twin bladed set up and the blades are stupidly expensive.