You could buy a mug warmer. I know those things exist, but I have no idea where you'd get one, and you'd have something electrical (probably a cord) around all that water which would make me feel uncomfortable. Otherwise a large bowl of hot water?
Here is an old post that had something similar to what may help your needs.
It was never reported on as to whether it was any good or not, I think from memory comments were that it was too big for whipping up lather.
They're big enough to whip up lather in, and heavy enough to just leave on the counter and have one hand free. They add an immense amount of luxury to my shaving routine.