Probably not long term. Plastic tanks are generally much more flexible than metal or composite. A short-term repair would be on the exterior and likely not be to your aesthetic approval.
You could possibly weld it, but being an original tank, it's probably all fragile.
I think new aftermarket tanks are available for the 200, but I'm not certain about the 350.
I'm not so certain climate controlled environments are best for the multitude of materials on vehicles. Humidity control for moisture/corrosion, and out of the weather or direct sunlight, but I think temperature swings are good for many materials as long as they're within limits. I know rubber components need to regularly see operational temps to keep the chemistry active.
Congrats on owning a BW350 though. I hope you can find a solution for the tank.