I have my entire cathedral ceiling in 8" T&G pine in the main part of my house.
You will be fine with the stove and the T&G.
Do put an air seal layer between the T&G & the bottom trusseschords/ceiling joists. Not plastic. Drywall, foam board, something that can truly be an air seal.
I am going through that right now. The PO I bought the house from just stapled the F/G batts between the bottom truss chords(instead of the bottom of the truss chords)leaving a gap between the insulation and the T&G. Bad deal, air flow like crazy and major heat loss. I am in the process of taking the T&G down, installing 2" foil faced polyiso board and, strapping under the iso then reinstall the T&G.
As long as you bring the wood in and let it acclimate with the house/room temp, you can install it. The wood with shrink & swell as the temps & humidity raise and lower, regardless of time of year.
Do make sure to leave at about a 1/4" gap around the perimeter of the wood for expansion when it does expand. I have installed all T&G in my addition, ceilings, walls and will reinstall the main house ceiling again in T&G, and have never had any issues with warpage. I highly suggest you finish the board in whatever finish you decide prior to installing. It really sucks doing it after, I've done that, and it sucks.