An oven for cooking food, the oven comprising: an enclosure (2) for receiving the food to be heated and for containing a cooking atmosphere, the enclosure (2) comprising two horizontal walls forming respectively a bottom wall (9) and a top wall (10), interconnected by at least two vertical side walls (7, 8), the enclosure (2) being closed by at least one door (5) that is likewise vertical, and communicating with the outside via an exhaust opening (28) for exhausting gas inside the enclosure (2) and at a pressure above atmospheric pressure; and a heater device (11) for heating the cooking atmosphere.