I've never had the luxury of having a temperature control on my water supply in the darkroom anf in the Scottish borders the spring water supply that serves the farm I live on is very cold in the winter. Having said that I've never had a print stain in the 30 years that I've made prints.
My washing method is as follows:-
Fully fix the print for the manufacturers suggested time.
Place it in a tray attached to the cold water supply with just a trickle of water passing through.
When the next print is due to go into the trickle tray, remove the first into a holding tray of fresh water.
At the end of the printing session I pass all prints in the holding tray through a hypo clear bath for the recommended time and then into a cold water wash for 40 minutes.
All prints are then toned in either selenium or gold and given a further 20 minute wash.