A method of operating a thermal exchange engine having a thermal energy conduction surface and rotating elements in the vessel which form a plurality of closed working chambers which increase or decrease in volume as the rotating elements move. The method involves placing a phase change fluid in each of the working chambers and operating the vessel as on a closed cycle without addition of phase change fluid into the vessel or removal of phase change fluid from the vessel. The method involves applying thermal energy to the thermal energy conduction surface, thereby thermally increasing or decreasing a pressure inside at least one working chamber positioned adjacent to the thermal energy conduction surface, such that the change in pressure inside the at least one working chamber causes the rotating elements to move the at least one working chamber away from the thermal energy conduction surface.