A hot-gas reciprocating engine comprising at least three pistons which each separate a space of lower temperature and a space of higher temperature. Each space of lower temperature is each time connected, via a regenerator and a heat exchanger which is in heat-exchanging contact with a reservoir containing heat-accummulating material, to a space of higher temperature having volume variations which lead in phase as well as to a space of higher temperature having volume variations which lag in phase. The said connections include valves which are operated by means for selectively releasing one of the two connections, each of the pistons co-operating, by way of a drive rod, with a tiltable plate which is mounted on a rotatable shaft. When the connections between the spaces of lower temperature and the relevant spaces of higher temperature with volume variations which lag in phase are released, the valve control means take along the independently operable means for tilting the plate in order to tilt the plate further.