I need to cook food from the middle ages and bring it to school for a project. How can I keep the food warm without using innovative appliances?
A couple options spring to mind.
One way is, as ChrisH mentions, simple insulation, using layers of straw and blankets would be the most portable options. I also recall that during that time items could be kept warm by burying them, or using an earthen oven to trap heat and keep something warm for hours, but these will tend not to be portable :)
To seal a pot containing said food, you can make a simple dough and use it to seal a lid on to a pot - this will keep moisture trapped, keeping the food from drying out, as well as keeping some more heat in (from steam, instead of letting it out). Sealed pots were not really common in medieval times, metal pots would not be common or portable enough to use like this, but the basic principle was used, they would have food sealed in crusts. In this case, the crust would be broken into and the contents just spooned out, since many of the crusts, especially for larger dishes, were thick and tough, and might even be scorched on the outside from long or repeated cooking, not very tasty. They were not intended to be eaten as part of the dish, they might be used for breadcrumbs in a later dish or given away, as the crust would need to be sturdy, thick, able to seal the contents from air, and able to withstand the reheating process, and so the crust wouldn't need, or want, to be tender or flavorful or even part of the dish in its own right.
Another thing you might try, in addition to insulation, would be to store and add heat either while traveling or afterwards - something like a hot water bottle, though at that level of technology it would more likely be hot rocks, which would work to keep the food warm. Depending on the insulation, method of travel, and dish involved they could even let the dish continue cooking while it traveled - something like stew or beans would be better for this, or really any dishes with extended cooking times. If you have enough rocks (enough thermal mass) in a very well-insulated container, they could stay hot for hours, likely enough to warm the food once you're ready to set up. You could try adding water to them once the food's set up over them, this would let the heat transfer quickly through steam or boiling water. Transporting hot rocks, etc, with the food container will keep everything hot longer, transporting them separately will mean the food won't keep cooking while in transit, for more delicate dishes.