I would absolutely recommend a diesel heater. I have 3 of them I use for ice fishing. Two are build into my permanent shacks and I have a portable one I use in my pop-up ice shack. They work great, and it wouldn't take much to set it up with either an external tank or a quick disconnect so you could fill the tank outside. For the little bit I use mine, I just use kerosene so it's not a big deal if I spill a little while filling the tanks inside. They sip the diesel/kerosene compared to propane. Can run all day on a gallon of fuel.

Keep in mind though they need a power source. I use a 12v lithium battery. A battery like that could last 2-3 days depending on how high you have it running.

There are some that have a control panel that works on either thermostat or manual level control. There was a thread on diesel heaters not too long ago, might find some more info and endorsements if you can track that down.