Are you looking for a temporary or permanent solution?

I should say short-term. If I install it, I won't remove it. But how much I will need it after this winter is not certain. If I were to heat the whole garage, to keep the car warm, then it would be a bigger investment and I would probably go for the heat pump.

I think you'd be trying to swim upstream in a rapidly flowing river, to try to heat any portion of an uninsulated structure that needs heat for comfort when occupied.

Update - the temperature is now -6°F! I know Air-sourced heat pumps are not very efficient at those temps, but this is the lowest temperature in over a year! I'm not trying to get a comfortable living space, just a tolerable one. Where the snow and ice on my car and snow blower can melt overnight!

Here is a heater which puts out 40,000 BTU for less than $100 plus the cost of a propane tank.

https://www.homedepot.com/p/Dyna-Glo-40-000-BTU-360-Degree-Tank-Top-Gas-Portable-Heater-TT40000M/307748429

That's of course unvented and not safe to use in a closed "indoor" space. Vented propane heaters with thermostatic controls for a permanent install aren't terribly expensive.

Have you considered wood? i worked on a farm,their shops were heated with wood.

How much warm do you need? Warm enough to store the car snug, to be out there while working on the car... or what?

Here, the pole barn is snug and dry- enough to keep the car in when it's winter. The barn has a wood burning stove in it- previous owners would run it and it worked to keep the cold off when they were working on a car in there. There's an insulated room in that barn that keeps even more steady, I think it's kind of a root cellar kind of deal. I've known home mecs that have had propane and electric heaters for while they were working. Some greenhouse folks out here keep the frozen off with propane run heaters that look kind of like old fashioned oil radiators.

If you know you are going to be spending time in the cold out there in the future. Consider insulation first, that will help greatly with any kind of heating you use.

Here is a wall mounted propane heater with a built in blower which can be unvented for $379. This could be connected to your propane tank. The output is advertised as 30,000 BTU,

https://www.homedepot.com/p/HearthSense-30-000-BTU-Unvented-Multiple-Fuel-Infrared-Plaque-Heater-With-Base-and-Blower-T-Stat-Control-Furnace-140326/313801095#overlay

Unvented propane or natural gas heaters are inexpensive to buy,even less expensive used and lowest operating cost you will find. Many construction crews use kerosene and diesel heaters but the odor is pretty bad.

I would like a heater that I can safely leave on overnight, unattended.

Yeah, if you want a heater you can safely leave on overnight in the garage, you need something professionally installed- like a furnace or one of those split heaters they install in the wall.

You should not leave ANY stand alone heater running unattended overnight in your garage. You should not leave a heater running unattended, that's heater safety 101.

I grew up in (the snow belt of) upstate NY. Uninsulated workshops were typically heated by wood stoves which I recommend you consider for your application.