both chambers are tied to each other. the fridge doesn't cool independently from the freezer. it pulls "coolness" from the freezer side of the house. a fan.
I learned something from the Fridge Repair guy that just showed up at my house a couple of months ago. step one in DIY. clean the hell out of the cooling fins. shop vac. I took it to the next level and blew it out with compressed air from my garage compressor. the stuff that flew out, could choke the life out of any unit (tip, blow towards the wall
). he then said, to take a spray bottle and clean the compressor fan. I just blasted the fins of the fan and wiped. and repeat.
that alone got my fridge humming again. but for insurance he changed out the relay that is attached next to the big black round drum looking thing. it is the compressor starter relay if I remember correctly. he charged me $80, which is a lot considering he let me do most of the work. next time? oh, I got this.