A hot fluid expansion engine has a plurality of actuator modules arranged in a star configuration around a central shaft. Each module includes a drive piston defining a working chamber of variable volume in the first enclosure; a movable displacement piston subdividing a second enclosure into a low temperature chamber of variable volume and a high temperature chamber of variable volume with the high temperature chamber communicating with a unit of a fluid heater device and the low temperature chamber communicating with the working chamber; and a fluid circulation circuit extending between the fluid heater device and the working chamber. The drive piston and the displacement piston of each actuator module are connected to the central shaft via respective first and second eccentric transmission devices suitable for imparting reciprocating motion in translation to each of the pistons with a phase lag of 90°.