I'm sorry to break it to you but you can't store a useful amount of heat in 2 gallons of water. I figured about 2000 btu, given 8kg of water, 60 deg C temp drop. Maybe something like a 20kg block of iron at 400C? gives you a much greater change in temp. Probably need expensive insulation though...
Probably your best bet is just get warm clothes, -100 boots, a real parka, and some sort of snow pants will have you hot enough that you won't need thick gloves to drive.
Also, how do you keep your windshield clear? Maybe you could install the rear window heating elements on the front window?
Or you could track down a volkswagon gasoline heater... Or install a small propane heater like this:
We have one with a hose for a bbq tank we use for ice fishing, runs for 48-110 hours depending on the setting. Has an 02 sensor that shuts it off if oxygen is getting low and also shuts off if you knock it over.
Ian