That covered dog carrier may seem like a dandy brooder, but it will be more like an oven, tending to be much too warm since there isn't much room in it for the chicks to find cool spaces. Rule of thumb is one square foot per chick when figuring out the size of your brooding area.
You would be much better off either getting a nice big cardboard appliance box, like a refrigerator comes in, or just brood directly in your coop or run.
The point to having a heat source is to provide a very small warming station for the chicks, and the entire remainder of their brooding space should be between 70 and 75F. Or even cooler if you're brooding outdoors, which is what I highly recommend.
I also recommend using a heating pad instead of a heat lamp. That way you will pretty much assure the chicks will not get overheated, which is a much bigger danger than having their space on the cool side.
I wrote an article for BYC on the advantages of brooding outdoors. It's linked below this post.