I used a rubbermaid container for my chicks as well. I didn't bother covering it for the first week or two, as they were too little to get out. I hung the heat lamp on a nearby cabinet and fastened it with like 3-4 pinch clamps. The thing never moved until I smacked my head on it and the actual lamp clamp fell apart. Haha! It hurt so much. But after the stars disappeared I grabbed a wrench and fixed it easily.
When the fuzzy butts got big enough to consider getting out of the rubbermaid tub I just used a dog gate laid over the top as my cover. It worked great for me.
The one other thing I did was to raise the brooder off the floor with two 4x4s holding a piece of plysood off the floor that I placed the tub on. I did this because my brooder was kept in an unheated workshop built on a cement pad. The pad stays at about 50 degrees, and that was too cold for the first few weeks.
I can't wait to see pictures of your fuzzy butts!