A haybox is essentially an old-timey crock pot, and is still an energy efficient way of cooking food. A large box (or other lidded container) is lined with hay (or other form of insulation). One then puts the food into a pot, brings it to a boil on a traditional stove or over a fire. Once the food is at cooking temperature, one removes the pot, and places it in the haybox. The initial heat is trapped in the haybox, so no further heating is required to cook the food.
A haybox does not need to be made from hay and a box, of course. You could use a hole in the ground and dried grass, or fiberglass insulation in a specially built cabinet. The box doesn't even need to be a rigid structure; in a pinch some people have used a sleeping bag filled with pillows. The important part of the haybox cooker is the insulation. It must both be reasonably insulative and be sufficiently fire resistant. While this second requirement is very important, it is usually only necessary to use a substance that will not burn (or offgas anything nasty) at temperatures of around 100 °C (212 °F), the boiling point of water.
Using a Dutch oven or other heavy pot will improve cooking times, as the extra thermal mass will help trap heat. The pot should fit snugly into the interior of the haybox, and the insulation should be kept dry. There may also be a reflective layer between the pot and the insulation (aluminum foil or mylar) to help reflect the heat back to the pot. A tight fitting lid on the box will also increase cooking efficiency.
No matter how good your insulation is, you will need to make sure that your food has reached cooking temperature all the way through before you put it in the haybox. Grains should be cooked for at least 5 minutes before putting them into the haybox, and denser or larger foods, such as beans and potatoes, should be cooked for as much as 15 minutes to make sure they are heated to the core.
Cooking times vary, depending on what you're cooking and the efficiency of your box. Foods will usually have to cook longer in a haybox than on a stovetop, sometimes as much as twice as long. You will have to experiment to get your cooking times right. While hayboxes are great for rice, beans, porridge, and the like, they are also used in the same fashion as crock pots; put the stew in at noon and take it out for dinner. You don't want to be opening your haybox to be checking on the food, so plan on meals that don't require precise cooking times.
Food cooked in hayboxes will also lose less water through evaporation than will other cooking methods, so measure your water short. A good rule of thumb is to reduce water by 25%, although this will depend on what you are cooking.
Hayboxes can be a cheap and easy DIY project, and are a great way to reduce energy usage. While stovetop cooking and even modern crock pots must provide a constant stream of heat pouring through the food, a haybox traps the initial dose of heat, meaning that you need only a fraction of the energy to cook your food. While perhaps not quite as Earth-friendly as a solar cooker, hayboxes are still an excellent way to save energy.
And best of all, hayboxed pots never boil over or burn. You just can't beat that.