in aging, temp plays a large part. flavor changes, both melding of existing flavors & developement of new flavors, happen more quickly at warmer temps and more slowly at lower. keeping something at fridge temps and expected it to age is somewhat counterproductive or at least understand that it is a slow proposition. aging is best done at cellar temps mid-50's to mid-60's. keeping a stable temp is also important - wide temp swings are not good.
all that said, many of us don't have the luxury of a cellar and have to do the best we can. all my vintage/aging beer, mead, & cider is kept in a closet of my home - essential in the temp range of high 60's to low 70's you mentioned.
I'd opt for keeping it at the temp range you mentioned, not at low fridge temp, if you want the beverage to age. If you want it to remain much as it is, then keep it in the fridge and you'll have the least change. That said, I don't have a lot of experience with cider (though I enjoy it and have a few bottles aging).