An improvement is provided to a pressurized close-cycle machine that has a cold-end pressure vessel (70) and is of the type having a piston (60, 128) undergoing reciprocating linear motion within a cylinder containing a working fluid heated by conduction through a heater (52, 106) by heat from an external thermal source. The improvement includes a heat exchanger for cooling the working fluid, where the heat exchanger is disposed within the cold-end pressure vessel by welding or other methods. A coolant tube (130) is used to convey coolant through the heat exchanger.