A drive system based on cyclic conversion of thermal energy into mechanical or electrical energy by using a difference in temperature between at least two media and the contraction of a metal element with shape memory properties, and a method for generating energy using the drive system. The drive system has a first and a second store containing media at different temperatures, the second store having a passage opening through a bottom of a housing. The housing is a cylinder containing a liquid-tight and gas-tight cylinder piston dividing the cylinder into two cylinder spaces of variable volumes. One cylinder space contains the metal element and the other cylinder space contains a restoring element. The metal element is secured to the piston at a fixing point and to a fixing point within the second store so that the metal element is in contact with the medium of the second store.