When chicks get chilled, even if it is because they were lacking the brains or instinct to go back to the warm place, their immune system and the entire rest of their bodily functions get pulled down. I think their what little brains they have stop functioning too. So it is very easy for them to die even if they just had to run two feet to get into the warm area.
When you first got the chicks home, I would have gave them a heated area even if it was very warm out. I would have given them the option to go into a the warming area. When putting them outside for the first time, They need a small area or they seem to get lost and not always are able to find their spot. I use a cut in half 275 gallon liquid tote as a brooder about 40 inches by 48 inches. I also always give them a light for the first couple of nights or a week so they come back to the warm place in the brooder and don't go huddle in a corner and pile up on each other and die. No light and sometimes they just can't seem to find their way to the warm spot. When I give the chicks the run of the coop, I will give them a warm spot even if it is summer time. If I am brooding in early spring, fall or winter, I turn my liquid tote brooder up side down and I put a light in it. I use an LED light white. I hang it inside the brooder from some wires sticking through the sides. I lift the sides up about 4 inches with some boards so the chicks can run in and out when they want to. I also have warm spot in there for them. So it is always warmer under the brooder. I have used this even in January and February here in Central Ohio very successfully. I sometimes even brood day old chicks in chicken tractors in April with my brooder plates. I cover the ends of the chicken tractor with plastic and since it has a solid roof, the chicks stay warm.
Now for my big suggestion. Ditch the heat lamp for the warm spot. Heat lamps are energy hogs usually over 200 watts. Probably over 5 years ago, I stopped using heat lamps. I bought a brooder plate from Premier 1. I wasn't sure at the time if I would like it but even the big one which is the one I bought only uses 40 to 60 watts. Darn near no fire hazard. I know that brooder plates cost more, but I think they work so much better. Mine have legs that you adjust for the height of the chicks. As the chicks get bigger you raise the legs. If you have the legs adjusted to the correct height, which is just about the height of the chicks back it keeps the chicks from piling on each other. If you raise cornish rock crosses, this saves a lot of chicks. I have been using the same brooder plates for over 5 years. I used to have to buy new heat lamp bulbs at about 10 bucks each every year because the darn things don't last long. I use so much less electricity with the brooder plates, I know they have paid for themselves easily. I have three of the ones that can handle 50 chicks each and I have one little one that handles ten chicks. I use the little one in the house in a small tote when I have eggs hatching in my incubators. I raise and sell replacement pullets and roosters for people to butcher. I have had one of my chicken tractors blown away over a fence with the brooder plate inside. I had to replace the cord on the brooder plate, but other than that it is still functioning fine. There were no chicks in the chicken tractor at the time. We had 70 mile an hour gusts that day.
I have also started using Oregano Essential Oil in the chick waterer to combat coccidia. IT seems to help a lot.
I also raise goats. I don't use heat lamps for my kids in the winter. I have heard too many horror stories about the barn burning down. I use heat mats. When it is really cold. The mats lay on the floor and the kids and even the momma goat can lay on them mat without hurting it. I have been using the same heat mats for over 7 years for my goats. The heat mats use about 40 to 60 watts depending on the size of the mat and in the spring, I sometimes use them to help germinate seeds. The heat mats I buy I got at rural king and they are for dogs to use in the winter in their dog house. I think you can order them on Amazon. I don't worry about my goat barn well really the goat hoop house, burning down.
I really consider the brooder plates and the heating mats as game changers in raising livestock. I have heard that some people have had their house burn down from heat lamps in the chick brooder. The brooder plates just dont get that hot. You can safely put your hand on the plate when it is warm.
Anyhow, goodluck with your chicks and I hope you don't have any more problems.