You might be able to make some wooden frames from 2''X1'' planed timber or similar, and fill them in with small-gauge (1/2'') mesh. Then, on the inside, fix sheets of cardboard or whatever you had handy, to retain the heat and prevent it leaking out of the sides. Then fix the panels together strongly, either with hinges, or just tie them with wire or nylon cord. Make a mesh panel, or a pair of hinged mesh panels, to cover the roof, and when in place, put a couple of heavy bricks on the corners to hold the whole frame down so the rats can't get under the edges. Presumably the floor is concrete, so as long as they couldn't get under the sides they wouldn't be able to dig their way in? You would need to make the sides low enough so that the heat lamp could be suspended above it in the early stages when it needs to be quite low, as the lamp wouldn't go through the panels over the top. Or just put in an electric hen of course.
If you browsed round the recycling centre skips, you might be able to find some kind of materials which are already a solid surface which could be used as one or more of the sides, eg an old door or cupboard fronts etc. Or place the brooder so that one side, and maybe even two, is formed by the sides of the garage walls, and then enclose it with two more sides to make a rectangular one, or one long side (old door?) for a triangle.