The cooler it is, the longer it may take to completely carb, but like frazier said: it depends.
I worried a lot about bottle conditioning temps at first because during the summer, even in my downstairs closet where I keep the beer, it gets pretty darned hot. I wouldn't be surprised if it reaches 80-90 degrees in there. Even during the cooler parts of summer, I'm probably lucky to have it around 70-80 degrees.
I haven't had any bottle bombs, nor have I experienced any off flavors or uneven carbonation or anything like that. I think bottle conditioning temps are probably more forgiving than fermentation temps.
One things I make sure to do however is consider the temperature they condition at when I calculate the volumes of co2 I want, so I get the appropriate amount of priming sugar. In other words, I may have different amounts of priming sugar to carb the same beer in summer versus winter.