That makes sense.
I've seen plans for an "Ohio brooder" that is a heat lamp mounted in a wooden box-- probably a very similar idea.
As long as the chicks are free to run in and out of the barrel, it would probably work fine.
While they are young and the weather is chilly, I would make sure the wind does not blow hard through the rest of the pen either. The wire mesh will slow the wind some, but it would probably be good to provide a windbreak of some sort as well. That could be a bale of hay inside so they can go behind it, or tarp on part of the outside, or whatever else works. I've read of people using empty feed bags, and I've even used pieces of cardboard sometimes (if I secure it right, cardboard will often last for at least a few weeks, even if it gets rained on. And by then, the chicks are enough bigger that it isn't needed.)