Normally hea-reflacting films are applied to glass to keep infrared radiation outside the house. But what if you'd apply it to the other side of the glass to keep infrared radiation in? (Not sure if this would work; I haven't seen the most recent films in action)

Another approach might be to put a blanket of fiberglass or stone wool insulation on top of the cold frame windows at night. But this is of course an extra to-do item twice a day.

I've been keeping track of the temps in my cold frame as well, but mine is not attached like yours to the house. It sits outside in one of the raised beds that have concrete around the edges and has two one-gallon glass containers filled with water and black paint. On March 8th the low was 30 degrees in it, but the last week the low has been 40. Just perfect for hardening off my brassicas and lettuce, which I am now transferring to the raised beds.

Maybe painting the concrete black would assist with heat retention?

I am a big fan of cold frames. We had several on the south side of our house in the mountains, and even with outside temps in the single digits, and a couple of times below zero, I never lost a plant to the cold. The ones closest to the edges might have some frostbite on the leaves, but everything survived. I just put a couple of jugs of water inside mine tonight, since the temps are supposed to get down to near single digits. But I suspect they will be okay. Now, forgetting to open them on a warm day and burning all the plants to a crisp, that's a different story.