A system for heating and cooling the interior of a motor vehicle includes a first climate control device designed to heat or cool the front area of the interior, and a second climate control device designed to heat or cool the rear area of the interior. A first evaporator is connectable to a cooling circuit assigned to the first climate control device and a second evaporator is connectable to a second cooling circuit assigned to the second climate control device. The second evaporator is located in a latent storage in order to charge the latent storage with cold and the second climate control device contains a first heat exchanger designed to transfer the cold removed via the heat transfer medium circuit or the second cooling agent circuit from the latent storage for cooling of the rear area of the interior by an air flow.