If it helps, realize there's a difference between the time it takes to carb and condition a beer, and the storage process. Gravity and temp are the two most important factors in letting a beer carb and condition. 3 weeks @ 70 degrees is about the minimum time it takes for a normal gravity beer to come to carbonation. The higher the gravity and/or the lower the temp, and it will take longer.
And just because a beer is carbed, it doesn't necessarily mean the beer doesn't still taste bad. It may need more time to lose what we call greeness.
I discuss the process in this blog...
Of Patience and Bottle Conditioning.
After you reach the point where the beer is carbed to a level you like and tastes good, THEN you think about storage. Most of us just chill down a few bottles of beer at a time and drink them leaving the rest at room temp til they have more space in the fridge and are low (that's what I do), while others have the space to cellar their beer, move it to a cooler place til they need to restock the fridge, while others have room to fridge their entire batch (lucky bastiges). Either way doesn't matter.
It's only how you store the bottles before they are carbed/conditioned that the temp is more crucial to getting them done sooner.
But if it's below 70, it will take longer for them to be ready.