Cold water is just fine, it is the physical action of scrubbing your hands that flushes the virus down the plughole. Warm water is more comfortable but water hot enough to kill virus would scald your hands. Apparently 60 degrees C for a few minutes will do it, also use hand sanitiser but there is not one that has been proved to kill viruses of the Norovirus type.
Sorry, I’m old school. If I’ve been to the toilet or am about to eat, I want to wash my hands in HOT water