Have you ever tried heating your teardrop with hot water inside a 5 gallon bucket or small 5 gallon water cooler ? Maybe even a 2.5 gallon bucket might work.
If you are willing to do that it will work pretty well.
Here's the heat capacity / specific heat calculation
Specific heat of water = 4.18 Joule/ (gram deg C)
Mass of one gallon water = 3785 grams
Mass of five gallon water = 18,925 grams
Assume you bring the water to a boil before you go to bed, and overnight it cools down to 65 deg F ( 18 C)
That's a temperature change of 82 C.
Now we can march through the arithmetic of the formula for energy equals mass times specific heat times temperature change
Q = m x Cp x delta T
= (18,925) grams x (4.18) Joule/ (gram deg C) x (82) C
= 6,486,733 Joules
For our batteries we prefer to think of energy in watt* hours rather than joules, so lets convert the answer into those units:
(6,486,733) J x (1) watt hour/3,600 Joule = 1,802 watt hours.
The cooling bucket of water releases 1,802 watt hours of energy into the cabin
So a five gallon bucket of boiled water will release as much energy into the cabin as MntnDon says we ought to get from three typical batteries.
It's just another example of how small the energy capacity is for batteries compared with hydrocarbon fuels.
Two hundred years ago people used your approach with hot water bottles and bed warming pans holding hot rocks or bricks.
It will still work.