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Turning off the heat and letting the second story freeze???

I have a 2.5 story cabin (daylight basement, main floor +loft - tall ceilings, about 1,200 sf total) in remote Alaska where is gets very very cold in the winter, about -10 F average is common for a Nov-March, sometimes colder.

This will be my second winter with this cabin and looking for a more cost-effective way to manage in the winter. Right now, my main heating system is a toyostove in the basement, and supplemental electric baseboard heaters on the main floor. I leave the toyo turned on to about 65 and the door to the upstairs open so heat can transfer up, and leave the electric baseboard at about 60. I use the house about 2 weekends a month in the winter so it's a huge bummer to pay the fuel oil and electric bills to keep it heated while I'm not there (about $500/month in the winter, will be a lot more with year with gas prices where they are).

I am having a wood stove installed in a couple of weeks to help heat the home when im using it but what I would like to do is drain all my water lines for the winter and completely shut off the upstairs heat and let it freeze on the main floor, close the door between the basement and the upstairs and leave the Toyo turned down to 50. Then just use the wood stove to heat the upstairs when I'm there.

I am hoping this would keep the toyo from burning on full blast if closing the door confines the heat to just the basement and it's not cycling to heat the whole house anymore. But my fear is that the second floor will get so cold the cold floor will suck more heat out of the basement than if I just kept the electric baseboard turned on. There is no insulation or sheetrock in the basement ceiling, just exposed joists and the flooring above.

What do you think?

Thank you for your advice

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