Do you still have the lid for the container? If so, get some hardware cloth or cage wire. Also a few thin scraps of lumber, maybe 1.5" wide and pretty thin, about 3/8"-1/2". Take a Sharpie and scribe a line around the lid about 2-3" in from the edge. Using a sturdy box cutter or knife, cut out the plastic from the middle of the lid, leaving all the rim part that closes and enough extra to attach your mesh.
Lay the wire mesh on top. Use washers on the shortest wood screws you can find, with the screen on one side of the lid and the wood strips on the other to receive the screws.
If you have other animals you worry will jump up on the brooder, reinforce with a strip across the middle. Size this strip so the edges are supported by the bin when the lid is closed.
The biggest hassle is making sure you have a secure place to set the heat lamp over things. I don't think melting plastic is good for chicks! I hope this makes sense - it is a quick and easy way to make a carrier too, especially if you drill extra vent holes in the sides. It is especially easier to sterilize than wire cages, since the poopy part is solid plastic.