A beer or like alcohol beverage dispensing apparatus has a keg for containing the beverage. A keg dispensing device is connected through a top portion of the keg and extends to a bottom portion of the keg to draw the beverage from the keg adjacent the bottom portion. The apparatus has a cooling plate in heat transfer contacting relation with the bottom of the keg and also has a Peltier thermoelectric device connected to the cooling plate so as to extract heat from the cooling plate and thereby extract heat from the keg. The cooling apparatus has a first temperature sensor, mounted in heat sensing relation with a bottom portion of the keg and a second temperature sensor mounted in heat sensing relation with an upper portion of the keg. A controller controls the cooling apparatus in response to the first and second temperature sensors so as to control the operation of the cooling apparatus to extract heat from the bottom portion of the keg to lower and maintain the temperature of the beverage contained in the keg to a desired beverage serving temperature. The keg may comprise either steel, stainless steel or copper so as to provide a stratified cooling effect or may comprise aluminum so as to initially cool the beverage in the container in a more homogeneous manner.