I would try a heat plate rather than a heat lamp. I used one with mine and I had no issues with managing heat. You can adjust its height while they grow. It’s a bit more natural for them since it’s a bit more like a momma bird. They can also go out and explore and go back under when they’re cold. We were using an old rabbit cage for a brooder. It may be a bit more expensive. But check your local buy and sell pages. You might find one second hand.
https://www.brinsea.com/c-36-chick-brooders.aspx
https://www.brinsea.com/c-36-chick-brooders.aspx