It's not the cold that stops them from laying in the winter, it's the short hours of sunlight. Just putting in a regular light on a timer so they get around 14 hours of light would have the same effect.
By keeping heat in the coop, people are doing a disservice to their chickens for two reasons. Either they don't get a chance to acclimate to the cold and will suffer from cold if electricity is lost, or they do get a chance to grow their nice thick down coats, and then their keeper puts a heat lamp in the coop. Now they have these warm coats that they can't take off, and are uncomfortable because it's too warm. Think about it: put on all your winter gear. Everything you need to stay warm. Now go outside for an hour or two. Go tromp around in the snow, go do chores, whatever. Not too bad, is it? That's because you're properly dressed. Now come in the house. Don't take off your gear, though. Keep it all on for at least a couple of hours. How is it feeling now? I have had chickens in their unheated coop in -25* weather and not lost a bird. There are definitely other factors at play. How is your ventilation?
When I first started keeping chickens, I thought they had to be sealed up tight in the coop, with a heat lamp. I had problems with frostbite and respiratory problems every year. Now that I keep it well ventilated and not heated, they do so much better. Large combed birds will get frostbite, so I try to keep chickens with smaller combs and wattles. Keeping chickens has a steep learning curve.
How many chickens do you have? How big is your coop (in feet by feet)? Do you have any ventilation? (I don't even put the windows back in the coops until it's 20* or so. I will shut them when it hits zero. I leave the pop door open until it's in the teens below zero.) What do you have for bedding? How cold does it get where you live? Have you checked your birds for parasites? They can weaken a chicken and make it harder for them to survive the cold.