I helped to build a few wigwams back in tenth grade, as part of a project in which my history teacher had his classes build an imitation of the Nipmuc villages that dotted the area centuries ago. We did this with the help of a few Nipmucs who live in town. If the mats or other coverings are prepared ahead of time, a wigwam can be put together in a day by a small group of people.
I found these directions, which are basically what we did in high school (except we used layers of burlap):
And for the mats:
I can attest that these get quite hot with just a small fire going in them, even if you only have a thin layer of burlap for covering. With cattail mats, bark, and/or hides you’d barely need any fire at all to keep warm. I’m hoping to make one to live in this summer, and maybe I’ll even be able to make the mats in late summer.