No, not that kind of hot-boxing. This is Cottage Life, not High Times.
An old catering trick, the hot box is nothing more than a cleanish cooler lined with newspapers or cardboard, used to keep food hot until the guests—who all want to eat at the same time—are ready. The more thermal mass the food has (think brisket), the longer it will stay hot.
So, if your barbecue is ready way ahead of schedule, simply place the food in a foil pan, wrap it tightly with foil, and set it in the cooler. Pile some old beach towels on top, and close the lid tightly. Going into the box at around 190°F (88°C), a pork shoulder or a beef brisket can stay piping hot for hours. Monitor the internal temperature with a meat thermometer (if you have a digital wire thermometer, leave it in the meat and sneak the wire under the lid). Meat must remain above 140°F (60°C) to stay out of the bacterial danger zone, a.k.a. the worst barbecue party ever.