You should be able to run your furnace off that generator if it's got enough amperage. Take the cable that feeds the furnace out of the breaker box, wirenut a #14 cord on to it, and plug it in.
CY: I save old line cords from appliances, for reasons such as this.
I see a lot of temporary romex made cords used at summer festivals and fairs. Since it's plugged in and temporary I dont think it violates any codes. Most of these cords at these events are made by licensed electricians anyhow.
CY: I'm sure they are just fine. Ideally, they should be UF, which is ultra violent light resistant. But, they must work OK.
Last summer our county fair was during a severe heat spell, and the farmers who had cattle were running around 120 fans in the barns. Mostly those big fans with half-horse or larger motors. The electrician was struggling to make all kinds of temporary cords, and he was not pleased. In fact he plans to install more permanent outlets in those barns before the next fair. I guess those 5 days of the fair, where he was on call 24/7 must have wore him out.
CY: Wow, that'd a good reason for more power sockets. I bet they (cattle and man alike) went through a lot of water, also.
Those Mr. Heater infared heaters work well. I use one on my toolshed in winter. But they do need ventilation to be safe. My toolshed is
12X16, so it's not real big, but it's not insulated. But it stays pretty warm with that heater. I just start the heater an hour befoere I go in there to work.
CY: Mine is even less safe than a Mr. Heater catalytic. But, I figure Tim and I are non smokers, and we'll be in and out a lot, so we won't really be too badly exposed to monoxide.