Looking at the comments I think I will be alright with the big room. The total heat loss 12000 btus at 7deg f according to my load calc. The reason for this will be in addition to the code required ceiling insulation, I will be doing R30 spray foam covered with cellulose on the walls. It is a double studded wall system so it will not suffer from thermal bridging. I want to spray foam the roof deck in the attic above but that will create a few problems. First I dont think it is possible to get r38 on the underside of a 2x4 trussed roof. Second, I worry about the weight of r38 cellulose on the 2x4 trusses stretched 25feet as 24inch on center. I would probably be better off treating the ceiling as an interior wall and putting in R13 fiberglass, spray foaming the roof deck, and then somehow affixing R30 fiberglass to the underside of the spray foam. I could even add furring strips under the truss, then net, and blow R30+ of fiberglass against the spray foam. Again, I would rather use cellulose but that is going to be a lot of weight on those trusses.

Again, I would rather use cellulose but that is going to be a lot of weight on those trusses.

I'm sure that your truss provider can provide designs for any load. Stabilized cellulose will help in cases where load on the drywall is a concern.

It would be interesting to know how the cost of the fan + electricity + the cooling effect of air movement compares to just leaving it alone.

Any time you get a big temperature differential like that, the rate of heat loss goes way up, particularly in Winter. Not only do you slow down the heat loss in the atrium when you push it back down, but you are recycling the heat back down to the living spaces. The temperature really goes high up there when the wood stove is in operation. I think of the heat generated during that time as FREE, so it supports the fan, financially speaking.

The purpose of the atrium is actually to create a powerful cooling tower through stack effect so the passive solar doesn't get too hot in the Summer.