With temps still that low at night, I certainly would not recommend leaving them out there overnight. Even if temps never get below freezing and they thus survive, still, they will sit there and sulk until nighttime temps are substantially warmer than that. I think your best bet is to bring them out into the cold frame in the morning and take them back inside at sunset. Alternatively, you could put a lightbulb inside for warmth, but that's kind of a waste of power unless your schedule doesn't permit you to run them in and out every day.

Also beware that on days when it's 65 and sunny, the temperature inside the cold frame can easily exceed 100. If the weather report is for it to be warm and sunny, then be sure to prop the lid open somehow for the excess heat to escape.

Good luck!
-Diggity

Here is a link that might be useful: Garden Imperative