regulating temperature in cheap offset smokers

I recently acquired a cheaply made offset smoker, and-- ahead of the big event-- did a 'dry run' to get a feel for how it behaves. I think my biggest issue will be regulating temperature; the smoker is made out of thin-gauged metal that just doesn't have enough thermal mass to avoid quick swings out of my ideal zone.

I'm thinking about adding some thermal mass to the bottom of the cooking chamber... possibly rocks or man-made bricks. But obviously I don't want to add anything that will out-gas toxic gases when heated.

Am I on to a good idea here? And if so, what kinds of materials are recommended? I've seen 'refractory fire bricks', however I think the point of those is that they don't store much heat themselves, which means they aren't really helpful for my needs.