They should be quite okay at a constant 20C. The rot problem may be quite serious though. I brought some A. macrorrhizos with me from a previous home to my current one some years ago. The plants had been growing really well and grew very tall. However, in the new place after about a year the plants began to shrink. Finally I checked some out and the tubers were rotting. I tried the drying out and cinnamon but it never helped. But many of the plants are still there now over 10 years later, only very small. During the growing season they keep going only just ahead of the rot. When they slow down for the off season the rot stops too. So the plants remain tiny. I've put it down to some sort of soil fungus. But cutting off the rot and putting the plant in new bought soil has never fixed the problem. It seems when it's in the tubers it's in there for good. I did a lot of asking around but have never found a solution. So I hate to say it but the problem might have already been in the tubers when you bought them. All you can do is to keep trying to clean them up and put them into clean soil. Your problem may be quite different to mine but keep it in mind if you seem to be getting nowhere despite trying.