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I'd recommend looking into portable propane heaters like the Mr Heater units. Supposed to be safe for indoors, and they don't require any electricity. Using a battery bank for electric heat will run your battery flat in no time at all unless it is unwieldy large (and therefore expensive).
You really should be asking two questions: what will it take to bring the space up to temperature in a reasonable amount of time, and what would it take to keep it there?
My garage shop is insulated. I have an indoor-safe propane heater capable of 18,000 BTU (equivalent to about 4 120V heaters) that will bring the space up to temperature in a reasonable amount of time. After that, I maintain the temperature with a single electric heater. I'm assuming you won't be heating the space 24/7; you probably would want a propane heater for mornings like today.
For your size space, a fan-less electric heater would probably be enough maintain the temperature; I find fan noise objectionable in an office environment. Maybe you even splurge on an 120V electric baseboard heater that you could control with a wall-mounted thermostat for consistency.
First, be extremely careful. Many sources of heat will produce carbon monoxide, which is deadly.
A properly installed fireplace or wood stove is best. If you can't install those, you'll want kerosene or propane heater which are certified as safe for indoor use. This is the one I recommend.
I can second this for effectiveness and reliability. I'm not sure if it qualifies as the cheapest solution, but I've used the hell out of my Mr. Heater Big Buddy this winter.
Along with the heat from four oil lamps (for light) the Big Buddy kept my house above 68 degrees all night last night while the power was out (it got down to 3 degrees F last night!)
It can be mounted on the wall if needed.
I spent an additional $35 for the hose with regulator that lets you connect it to a large propane tank.
I bought this, HIGHLY recommended.
Also, I got 6mm plastic and lined all the ceiling and walls. Then got the $0.50/sq/f cheap carpet at home depot and line the floor and walls with it. insulates pretty decent.
Okay thanks. Just did a quick search for propane heaters, these look good [link]
I use this Mr. Heater. I also have a carbon monoxide detector in the room because I thought I would run into an issue. No issue so far. I love this heater and wouldn't change it for anything. It gets so hot in my garage room that I work out in shorts and t shirt and end up turning the heater off. I'm in Wisconsin.
Wool and linen. NO COTTON! Socks, tunics, scarves, gloves, hats. Lots of wool, and linen underneath.
Use a product like Montana Pitch Blend or Sno-Seal to make your boots water-resistant. Reapply regularly.
Propane heaters for unheated buildings! We have eight of these, they're great: [link]
Pace yourself, make sure you eat and drink, and go indoors for a warming break BEFORE you need to.
We gets lots of snow in upstate New York. :)
This works for me in NJ - [link]
This is on my wish list
Mr. Heater MH18B, Portable Propane Heater [link]
But I'll cook for you.
Yeah I am thinking op might actually have a propane heater, something like a Mr Heater