I wouldn't think cold temps would make your leaves droop I have let my temps go down in the 40's to bring out the purple in them. I would think if that is what going on is another problem to much or not enough of something? Maybe a puic would help?
do cold temp make leaves droop? I haven't noticed this effect before. But I tend not to let the temps get to low. I believe overnight the leaves tend to droop more or less because of the drop in water pressure in the plant.
I have new/baby plants that were exposed to 3 nights of 40 degree temps. Amazingly one is looking so good for a month, one fell over damn cats, and two others seem to be doin fair.