Like the o/p, over the years there have been the occasional winter heating question by those who aren't able to run a cable out to the van. I recall one question about using the leisure battery in the van to keep everything from freezing up. Most of us knew that using a leisure battery wouldn't work, but we had no figures to justify our answer - well I didn't anyway.
I have a 105 amp lithium phosphate battery on the van.
I also have a 700w 230v inverter recently purchased. I also have an 800 watt, 220v heater with an added frostat controller. Many years ago it was a wall heater which I have modified by adding a temperature controller, an on/off illuminated rocker switch and fitted it to a metal frame with caster wheels.
I plugged the heater into the inverter the other day to see what would happen. The inverter would only deliver 710 watt with the heater switched on. To supply that heater, the LifePO4 battery was delivering 58 amps to the inverter.
In theory, this combination would drain the battery in just less than 2 hours.
I also learnt the Chinese made inverter isn't able to live up to its advertised specs. Drawing 710 watts took about 3 minutes before the unit identified a fault and switched the inverter off. The inverter's cooling fan did kick on, but the inverter was pretty hot before the fan activated. The other thing is that the supplied cables got rather warm as well. I left the unit connected up, and the inverter fault light did switch off and the inverter started to supply power to the heater. I switched the unit off just after that, as the supply cables just go hotter, as they never fully cooled when the heater was off.