I do not know if there is one but you can make one.. I will describe
you need a 12 volt battery.. Can be lead acid or it can be a "Dry cell" (photo flash may well work) These are often used in Photographer's equipment and in some Smoke alarms.
You need an LED light string, one that has that "long running" feature you mentioned.. I have a pair I got at a store called Meijer (Mich, Oh, Ky) for like fifteen bucks, these are abut 5-6 inches long and either come on constant (My install) or "Chase" (the other option). (Chass means the light runs down the strip) I use 'em as step lights (Door open light on lights).
ANd a thermostat to sense low temp, One of the little DISC jobs should do, Electronics parts stores often have 'em in assorted temps
I do not think I need to tell you how to hook 'em up.
Ground---battery---Temp switch---LED---Ground.