As long as it doesn't freeze, the seeds will continue to mature, but more slowly once it cools down. I let most of my "Hot & Spicy" basil bloom as soon as it wanted to this summer -- and the seeds are STILL green on it! If necessary, I'll pull up plants and stuff them into a pot... they can hang out by a window until they mature.
I've even cut basil stems with nearly-mature seeds (a few pods with black seeds on the bottom of the stem, so I knew the others were close) and put them in a vase with water... I did get mature seeds that way, but probably 25% weren't good. I just marked the packets "sow thickly," and the seeds germinated well enough to product some plants, anyway.
