It will run the heater fine but kills the battery quicklyIt will run the heater fine but kills the battery quickly.
I cannot help further.
The heater motor is a big amp draw, but should run off and on all night then be dead by morning. I have two batteries and even when they were new the heater would draw down the voltage quickly. On very cold nights when it would run half the time both batts would be pretty low by morning and the lights would be half as dim,though I had an ARB electric fridge running too, but it would not draw a lot of power on a cold night.
I would take the battery in to a auto parts store and have them load test it. Those test are not perfect, but will possibly identify issues. They will also want to fully charge it with a high quality batt charger, so you leave it, let them charge it, then they test it. At the least you get a free quality charge…