The invention relates to a food-cooking or -heating appliance, and a method for cooking or heating food using the appliance. The appliance includes a tank (2) for a combustion liquid, a container (3) for food, and a support (1) for holding the tank (2) and the container (3) in position. The tank (2) includes a base (6) and a sidewall (7) inwardly inclined towards the top.