I believe a scuttle works better than a mug in a sink of hot water. My sink, at least, drains heat from the water rather quickly. My current solution - a shaving mug resting in an insulated food server with hot water - stays hot much longer. I'm sure a modern scuttle does an equally good job with more convenience.

The trick is to keep a temperature that feels hot to the face without drying out the lather. Hot tap water is just right.