A system for storing and outputting thermal energy and a method for operating the system are provided. The system has a heat accumulator and a cold accumulator. The heat accumulator and the cold accumulator are discharged in two separate discharging circuits, wherein the thermal energy is converted into electrical energy, for example by a generator. The residual heat from the process in the circuit can be advantageously fed to the process in the circuit by a first heat exchanger, whereby the total efficiency is advantageously improved. Furthermore, the heat from the heat accumulator can be advantageously transferred into the first circuit by a waste-heat steam generator. The heat accumulator and the cold accumulator can be charged, for example, with excess energy from the electric network by a motor. Excess energy reserves of alternative energy resources, for example, can thus be stored.