The Brits have science TV show call 'Bang Goes The Theory.' On a recent episode, they cooked a chicken with two bulbs in a space about that big.
Infrared lamps (food or otherwise), work by line of sight. In an enclosed space such as this, they wouldn't heat evenly. A regular bulb is perfect for the task.
Matthew, if possible, you might want to track down a smaller bulb. A smaller bulb will result in a greater range of rotation on the dimmer. This will let you mark off temps on the dimmer dial easier.