Liam et al, Re Dome heat plumes.
I tried A/C in my domed obs and I was not very satisfied with the result. It seemed the cold air inside the dome still was interacting with the external air causing issues. It was also expensive over time. When the A/C died, I decided to try a different tack - I installed a 18" variable speed exhaust fan in one wall. I turned it on high coming into evening and slowed it down later (so it was not too noisy). Drawing air into the dome seemed to stop plumes from forming and I experienced better seeing. On the other hand, there was a exhaust plume on one side of the observatory which did affect seeing in that direction (A/C, if running at night, are worse!).
The fan was reversible, I tried it blowing into the obs, that was seriously worse.
At a different site I had a slide off roof, the seeing was almost always better there. I also enjoyed the open aesthetic of the slide off roof, always more fun (mostly visual).
I think a dome wins when you want light/wind shielding esp imaging or for remote operation.