Since the purpose of the under sink lav water heater is to prevent wasting hot water, it seems to me that I should hook it to the cold supply. Otherwise, hot water will flow into the supply line and cool down, wasting it.

OTOH, is 2 1/2 gallons enough for a woman to wash her face, get her makeup off, etc? Maybe I'll have to crank up the thermostat setting a bit?

If she's going to use up more than a tank, then I'll need to hook it to the hot supply.