John_S:
Also, if you go too slow, you will be losing heat faster than the battery can put it in. Theoretically a 1.35W heater should be able to boil water. Realistically it won't even come close for any substantial amount of water.
Oh, yes. All those times assume perfect insulation.
33.333 Watt Hours from a 12V battery would be about 2.8 Amp Hours. You can get that size sealed lead-acid battery for under $20. Unfortunately that battery is rated 2.9 Ah at 20 hours. Without perfect insulation there is no way you are going to heat the water over 20 hours and get the same temperature rise. I think you will need a significantly larger battery, like a car battery. You can then buy a 200W car immersion heater to turn the charge in the battery into heat: Item detail page