I don't know how long you have since my brooder has a top, but I'd do it sooner rather than later. Time has a way of really flying past the way they grow. I've seen a broody hen get three day old chicks up into a nest about a foot off the ground, so they can go vertical pretty quickly if they are motivated. She tells them to come and they do. Once one figures how to escape, they all will learn pretty quickly.
A brooder that size should work great. I suggest you keep one area the right temperature and let the rest cool down as it will instead of trying to keep the entire brooder the perfect temperature. You don't have to worry about temperature and they will find their own comfort zone if you give them a choice.
I have my brooder out in the coop made totally out of wire, but I have a plastic drop cloth wrapped around the bottom to stop all drafts. The top half of the walls and the top are all wire so they get plenty of ventilation. One area is kept warm but the far corners cool off to whatever the ambient temperature is, often way below the "perfect" temperatures. You'd be surprised how much time even three day old chicks spend in the colder areas, only going back to the warm area occasionally. I think they are healthier and get acclimated much better if they have a range of temperatures. My brooder is 3' x 5', but your 2' x 4' should be plenty big enough to heat one area ansd let the rest cool off.
