I wouldn't think the steady 1.5a or so draw would bring down a hot vehicle battery overnight, that's 1/2 to 1/3 of what a 12v fridge pulls.
I'm going to completely disagree here, I'll go through it with actual power usages instead of instantaneous Amp measurements and show why...
I ran my Vevor diesel heater for 3 nights in a row, 13 to 16 hrs long, on back pati, hooked up to power station and multimeter.
Total power used for start up is 110W or so, for 6 minutes or less, so 1/10th an hour, so that is 11 Watt-hrs. Then running on setting 2 of 10, it is about 16-22W, say 20W. Running that for 12 hrs like you would for an evening plus sleep, would be 240 Watt-hrs, totalling 251 Watt-hrs.
At setting 6 of 10, total usage was about double, 495 Watt-hrs over 12 hrs.
A standard car battery, say a popular group24, is between 70 and 85 "Amp hrs" or Ah, at 12v nominal. You can only discharge a flooded lead acid car battery 50% without issues, and even at 50% discharge you will likely have problems starting car motor in the cold. So, a standard car battery has 40Ah usable at 12V, is 480 Watt-hrs. So running diesel heater overnight on 2 will drain a standard group24 car battery by 26%, or 52% of its usable power. Running heater at medium 6 setting will use 100% of the available power, about 50% of full battery.
That is too risky for me, in say 0 F weather, I want my engine to start the next day!
Notice how I used Watt-hrs up above, instead of Amps? I'm gonna be pedantic, I see people use incorrect units all the time talking about batteries and it just confuses things. So, I will point out that you don't discuss battery power usage, battery drain, or a battery's ability to handle a load overnight, using the current! Or the units current is measured in, Amps. Current or amperage are instantaneous measurements, and don't tell how much stored power was used nor how much a battery gets drained. And if you use Amps without ever saying what the voltage of your battery is, it's even worse. Instantaneous power is better, which is Watts or Amps x Volts, but even that is still not the correct unit.
The correct parameter is power usage, Measured in Watt-hrs. Battery power is measures in Watt-hrs. If you divide that by battery voltage, you get Amp-hrs, a much worse unit often used to label batteries because it is easily manipulated for marketing purposes to make a battery sound bigger. They never say if they used 12.8v for lead acid full battery, or 11.8 near bottom of its charge, or 13.8 for lithium etc, and of course they pick the lowest voltage they can get away with for marketing.
You can see how using Amps to discuss power usage causes mistakes in the comment above that diesel heater is using 1/2 to 1/3 of what dc fridge is "pulling". This in fact is not true... yes, a dc fridge will pull 40W when it is running, but the compressor only runs for short periods--again, why you measure power use over time, not instantaneous. So my dc fridge pulls 40W running, but when cold only runs for a few minutes an hour. Total usage over 12 hrs was 84 Watt-hrs, which is just 1/3 of what the diesel heater uses on setting 2! By looking at Amps, user above got mistaken idea a fridge used 9x that much power, and 3x what heater used, when it is actually the complete reverse. Heater on medium 6 setting uses 5.9 times as much power as fridge.