An energy system for ventilating and heating dwellings (1) comprises an air to water exhaust heat pump (8) which draws fresh air (13) in through openings (12) in the outer wall (11) of the dwelling in clean residence rooms such as living room (2) and bedroom (4), and out through dirty rooms such as bathroom (5) and kitchen (3) as warm used air (24) on the way to the heat pump (8). The heat pump (8) supplies warm water (25) to radiators (14) located in clean rooms (2, 4) and supplies cooled used air to a discharge (10). The radiators are placed adjacent the openings (12) in the outer wall (11), so that the fresh air (13) has to pass the radiators (14) and be warmed on its way into the room. This avoids cold draft from the fresh air, and the efficiency of the heat pump is optimalized. The heat pump (8) also supplies warm water (26) for heating tap water (28) in a hot water container (27).