I use plastic grocery store bags because the tubers do want some humidity or they'll start that awful shrinking process. I do not want the bag closed tight so they can breathe.
The eyes will obviously always be a mystery to me so I dig clumps, huge and small and each one gets the name on the bag as well as a label inside the bag. That way I'll be ready to plant when warm enough temperatures come along. With clumps there is no way to enclose the entire thing in Saran Wrap and people have had mixed results. It mostly depends on the condition of the tuber at the time it gets wrapped.
I do put a thermometer at the top of the bag but it's all covered with scatter rugs and a tarp. I check now and then, not on a regular basis.
