Holding bottles at cooler temp - effect on carbonation?

I've had my first brew in the bottle for three weeks, and cracked one open last night (cooled in the fridge first) - there was good head, but not a lot of bubbles in suspension. My bottles have been in a muck bucket, coverd with a towel on a cabinet in my basement - the temps hoover between about 60-65 deg. I fermented here as well (APA), and had no issues - fermentation finished in about 3 days, moved to secondary after 7.

I'm assuming that if I give them another week or so, they will carbonate fine - assuming the yeast is working, just working slower.....

Is that right, or am I off base? Hopefully, that is correct, I really don't have a warmer place to store them.

Sorry if this is a "dead horse" topic - I tried the search, but didn't find what I was looking for...

You are correct. They just need a little more time.

I was storing my first batch (blond ale) at 60-62* during carbonation and after two weeks I popped the top on the first bottle (after 2 weeks in bottles) and, although it was carbonated, it was still a little flat. It has been two weeks since then and each bottle I have of it seems to be more and more carbonated. So I would just give it some more time. the temps we are carbonating at, seem to take quite a while to get it carbonated. Good luck and happy brewing.