Force carbonating

I'm picking up a dual keg system next month and will use it in converted fridge. CO2 tank has dual regulators allowing control over 2 kegs at once. My question is, as this unit will be sitting in the fridge, can I force carbonate one beer in the fridge while drinking the other, or do I need to force carbonate at room temp? If it has to be outside of the fridge, how to I structure my setup to do this? Do I just buy another CO2 tank? Seems silly being I already have a dual tank.

Thanks in advance.

Put them both on serving pressure in the fridge. Drink one for three weeks and then the other will be finished.

It's better to carb at lower temperatures. You use less gas.

Agreed with bad brew. If you have the room, put everything in the fridge and set to serving pressure all will equal out in about 10 days in my experience. Also, the time will help to clarify the beer. If the one keg has to be outside the fridge, no problem. There are some differences in the amount of dissolved CO2 at the temp the liquid is at but you can adjust later if needed. Just remember it will still take a week to get the keg cold once moved into the fridge.

As stated, you're better off carbonating when the beer is already cold. With the dual regulators you can force carb one while serving the other. If you set them both to serving pressure it will take 10-14 days to carbonate from my experience. If you want it to carb faster, just turn the pressure up on the one you are wanting to carbonate quicker to about 30psi for a day or two and start checking it. You can get it fully carbed in just a couple days.

I cold crash my beers and hook to 30 psi and shake it for about 45 seconds, disconnect from the CO2 and let it sit in the fridge overnight. When I check it the next day the beer is mostly carbonated but is still a little green so I just hook it back up to normal serving pressure and give it a few more days to stabilize. Got it down to science after six years worth of kegging.

Put CO2 stones in your kegs (cost about $17 for stone and a 2' piece of hose), you can carb in 2 days at serving pressure/temp. No need to wait two weeks for it or mess with jacking pressure up and down, venting the keg, etc.