I remember seeing something like that on youtube, the guy in the video said it significantly helped his prints. I’ll see if I can find it, but that was 8 months ago.
Edit: Here are a couple videos, neither of them are the one I saw, but they both seem to support the general idea of an enclosure/heated chamber.
I understand his need to vent noxious fumes and it will probably become an issue for me when I get my printer going. It would be a good idea if the vent ing was thermostatically controlled though as continually extracting air outside would cool the chamber. Also in the cold white north [currently -20 c] you would only want to exhaust over temp air outside. Seems with an acoustic lining the noise would be reduced as well !
Having a fixed cabinet would also give mounting points for extras ie. webcam, lighting etc…
I have my cubical reprap enclosed in polycarbonate (Plexiglas). It does help with warp (no wonders but quite a bit of help for larger prints) and i added an exhaust vent with a charcoal filter to reduce ABS smell. The chamber keeps the inner temperature @ 50°C without any extra heating.
My chamber helps especially with large prints - I used to have the edges curl up on the front/back of the Y axis (using a Prusa where that bit moves about a lot), heated chamber fixed that.
I’d imagine it would be a little bit less dramatic on the Thing-o-matic, but it should help some. Just make sure your electronics are still well cooled, I’m not sure where the live on that bot.