Actually, I like raising chicks in 50F or cooler unheated garage. As long as the temp under the heat lamp is correct and there's enough space for everyone to get warm at once if they want/need to, raising in a cold garage helps them acclimate to the outdoor temperatures so it's not much of a shock when at 4-6 weeks they go outside into the coop/run without a heat lamp. It's like mom has kicked them out to be juveniles because they have all their feathers. Just keep an eye on them, they should be alert enough and warm enough to dash over to the food and water and eat or drink, then back under the heat lamp, like they would a hen. If they just stay under the heat lamp all day without periodic excursions, then I'd look at enclosing the brooder more to capture more of the ambient heat from the lamp, raising the local temperature for the chicks. If they stay at the edges of the enclosure all the time, then your heat lamp area is too hot for them, raise your lamp and/or get more ambient air exchange in your brooder.
I use a ~3 ft by ~3 ft by 4 ft wire dog crate, line the inside and half-way up with old feedbags to keep the shavings in, and put the dog crate pan in the bottom to hold the shavings. If I think they're too cold, I'll put strips of wood or aluminum foil over the top of the crate (where the chicks can't get it) to reflect more heat back into the enclosure. Firewood and aluminum foil and firewood loosely wrapped with aluminum foil is great for keeping heat lamp light away from anything plastic, blocking lamp light, reflecting it back, or providing a barrier on top of the crate. The aluminum dissipates the heat so the wood doesn't get too hot, and the wood is already less sensitive than anything plastic in the setup to temperature.
I raised 25 CX in my garage one year starting in early January (waaay to early, but I didn't know and they were on sale), and this method worked fine. Other times, I've raised them in March or so, but those Jan chicks were perfectly healthy and dealt well with this setup, which is awesome considering they were meat birds, and prone to health issues if not adequately managed. (For the 25 CX, i used 2 crates put together so they'd have enough room, with a goal of getting them outside at 4 weeks.)