I've been toying with the solar route as we have plenty of sun in these parts. A box lined with foil or black insides maybe, with a clear top, and a small computer fan on a timer to cycle the the air out every 24 hrs. You know how hot it gets in a car in the sun? hummm....
I might have to do some small scale tests-laser thermometer etc.
On your oil heater just watch your CO levels(even if it's ventilated as with a tight enclosure it may not draft so well)-you won't get a second chance on either: Oxygen deficient environments or Carbon monoxide. I've had the oxygen deficient experience and I can tell you it'll be lights out so quick you'll never know what hit you-seriously. Same with CO because it, at the higher levels will eliminate the abilty for your lungs to convert oxygen into your bloodstream with the exact same effect as insufficient oxygen. The only difference is with a slow rise you will probably experience symptoms such as nausea with the CO but not in this case within a confined space. Well won't the heater go out? Yes, but the CO & O2 levels in the room can stay the same for an extended period. I'm not intending to condescend, just inform. You can do this safely, just completely ventilate before you go in but watch the kids and those unaware also. Good luck-keep us posted.
An additional bit on CO the levels in your bloodstream can build up slowly over a period of hours or days and still kill you. This is because it doesn't easily clear out of your system but takes time.