Vine that withstands freezing roots

I am looking for a vine that can withstand the cold in Zone 5 (Chicago) in containers. I have 2 copper pots that are approx 36" high and 16" square at the top (tapers down to base of about 8 " square). I am looking to grow a vine (preferably fast growing) on a large trellis and there is nowhere other than these pots to put it. I tried grape vines and a couple of other things and they didn't make it through winter. The location gets partial to full sun. The two pots need to cover a trellis approx 20 feet long and 2 feet high above my fence.
I was considering clematis, but think that the metal containers will make the roots get too warm, which I know they don't like.
Thanks
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I don't know that you have a chance to grow any vine in there. The pots are small for a vine, first of all. Second, you are right that you lose a lot of zones when you leave plants in pots outside. Just to give you an idea, I lost all the lemon balm that I had planted in a much larger pot outside (2.5 feet in each direction), with good thermal contact to the ground, and lemon balm is hardier than grapes (and I live near Detroit, which is warmer than Chicago). But the jujube which is in the pot survives and thrives to this day. So, I am guessing that anything hardy to Zone 3 will survive - I know of no vines that hardy. Perhaps an annual vine, such as sweet potato? That way you can change the soil every year and have it prosper.
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I guess a possibility is growing something that gets cut back in the fall and moving the pots to my garage. It is not heated, but will be protected from the wind. I would need something that grows very quickly though to cover the length of my trellis if it is going to start from scratch each sprint.
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In article snipped-for-privacy@hotmail.com says...

Morning Glories are excellent fast growing vines. I grow a lot of them in pots and if started early, like now, they can climb more than 15 feet. They also provide nice foliage. I can get 3 plants going in a 12"x12"x16"(high) pot with no problem. They do however need to be watered practically every night during the summer which can be a PITA after awhile.
I was thinking of growing grapes in large pots here in Chicago but it appears that may not be possible. I'm building a permanent trellis system and hoped to populate that with a grape vine that would take many years to grow. Oh well.
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