I usually condition my ales in the closet at about 70 degrees. That way they can sufficiently carbonate. I usually leave them there until I move them to the fridge to consume them. They usually condition in the closet for at least 2 to 4 weeks. If you are brewing a lager or pilsener and are using an appropriate lager yeast, they are aged for much longer at much lower temperatures and usually require refridgeration during the conditioning phase.
The lower the temperature and the longer it'll take to carbonate and condition. I find after about 4 weeks the beer is perfect at around the 75F mark. And I only put the bottles in the fridge the morning of the day I will drink them.
If the beer has aged long enough, sometimes I will move it to the fridge to stop the aging process and make the remaining yeast fall out of suspension. As beer ages it becomes a little more dry in flavor and cold temperatures will stop the process for ales. Lagers may continue to slowly age due to the low temperature tolerances of lager yeasts. But in any case this effect is barely noticable and should not be worried about.
If you're doing natural bottle conditioning, then you need to store the bottles at the same temperature you fermented at. Remember what is going on here is that the beer is fermenting just a bit more to carbonate the beer. After a couple of weeks, you can chill the beer, and I would say that is the best way to store it once the conditioning is over.