when you dig them up, let the earth dry on them for a few days...never store them wet. Get some fresh peat moss or potting mix, toss in a bit of sulfur (great antifungal agent), put your rhizomes in a plastic bag with this peat/sulfur mix and toss them gently in it to get a coating on them. do not close the bags, just loosely fold the tops over. Store them in the dark in a cooler temperature....below 60 F. they should keep just fine. check them once or twice in the winter and remove any that appear to be rotting.....but the peat and sulfur should reduce the mortality rate significantly.

68 degrees is too hot.

What I did last year, was treat them similar to how I treated my dahlia tubers.
1) Like Don say, dig them carefully. I clean the soil off of them and let them dry for a day or so. Never store them wet.
2) put them into a bag with a fungicide or some sort, and coat them well, .... like shake and bake. LOL
3) Here is where I differ. Then I wrapped them tightly in saran wrap and labelled the type and colour of the tuber.
4) these I placed into paper bag, and then wrapped loosely with old newspaper, and then placed them into a cardboard box.
5) I stored the cardboard box of tubers, in my cold cellar, but was absolutely certain that it did not freeze. Below 55 degrees is good, but above 35 degrees.
I lost NONE.

.... just an idea

Here is a link that might be useful: check out the end of this link

Would storing in the refrigerator work? We have a fridge in the basement and I've used it for storing tulips and daff bulbs.