Hmmm...I have a batch of hefe sitting at home right now but I can't recall exactly when I bottled it, I will check that when I get home. I know its been in the bottle at least 4 weeks and I think a couple more. I've been drinking it since it was 3 weeks in the bottle but only adding bottles to the fridge as necessary. The carbonation is a little screwy, big bubbles, but aside from that it's tasted great since 3 weeks in.
I will try this as an experiment. I have a couple bottles that have been in the fridge since week 3 and a case that has been sitting in a closet in my basement for the same amount of time. Tonight when I get home I'll throw a bottle that's been sitting in the closet into the fridge just to chill it for a couple hours and then pour a glass of it beside a glass of the stuff that's been in the fridge for several weeks and see if there's a difference in flavor, head, etc. I can hold on to a couple other bottles and perform the same test in a couple weeks. I will report back what I find.