when you dont need to waste 2 hours a day on processing and hauling wood, that saves you a lot of calories otherwise wasted out in the cold. That's a big deal over 100 days and an essential for lasting 200 days.
once you've got the igloo, you dont need the double layered tarp shelter any more, So it can be folded in half, stuffed with more debris, wrapped around you, all of your clothing, the poncho and leggings made of tarp, and the 10x10 tarp, with dry debris between each layer. That's a helluva lot of insulation, added to the sealed, reflective and insulative igoo. So no, you dont need a warming fire. Yes, the Innuit had caribou and seal hides, but they needed remain mobile, so that they could move to another area if the seal hunting got bad. Insulation is provided trapped air. It doesnt matter how you GET that trapped air. It can be done with the hollow hairs of arctic animals and their hides, with a goose down sleeping bag, or with lots of layers of debris and impermeable fabric. The effect is the same. You dont lose body heat. So the issue becomes one of providing enough food to maintain your body's normal self-heating metabolism.