Use of fermentation chamber after hit required gravity

I have recently connected an Inkbird controller to a fridge and I am using it for the first time to control the fermentation temperature of a pale ale. I'm now at day 6 of the fermentation and I've hit the target gravity of 1008. All airlock activity has stopped and I'm assuming the yeast are on clean-up at the moment. In fact the target gravity was reached after three days (using Nottingham yeast and keeping temperatures in the range of 18-20 degrees C).

Do I still need to control the temperature now I've hit my target gravity and all activity has stopped? Can I remove the fermenter from the fridge and replace it with a new brew?

Do you plan to chill the beer?

I intend to cold crash it before bottling, but I can schedule my different brews so that the fermentation chamber is free when that needs to happen, and just swap them out if the chamber is occupied.

I normally let the yeast clean up at around 20-22C (room temp) for a week. In other words, I leave the FV for two weeks then crash cool for a week.

Okay, thanks.

2 days at 14c after ferment to remove diacetyl (not much of that in Nottingham but loads in s-04) then cold crash to drop excess yeast out. You want to check for diacetyl and sulfur after ferment, both won't go away once packaged!