Heat lamps are a major fire hazard. Most breeds are cold hardy, so they'll be fine down to negative temps. A roller coaster of temps will negatively impact their health, which having a heat lamp in is doing. Shortening day light is why affects laying, so if you want to supplement light to...
What are their ages, are they molting? Have you checked for mites? It's likely just the shorter days. I would get the heat lamp out ASAP. Chickens don't need heat and it could be stressing your birds, which would stop production.