Abstract: A method and apparatus for converting thermal energy into mechanical work, whereby first (4) and second devices (9) for storing thermal energy are alternately connected into a turbine branch (T). In order to increase efficiency, a compressed oxidizing gas (11) is cooled to a second temperature T2 before passing through the first device (4) for storing thermal energy, and the oxidizing gas is then increased, in one step, to a third temperature T3 when passing through the first device (4) for storing thermal energy.