This article presents a framework that describes formally the underlying unsteady and conjugate heat transfer processes that are undergone in thermodynamic systems, along with results from its application to the characterisation of the reciprocating compression and expansion processes in a gas spring. Specifically, a heat transfer model is proposed that solves the one-dimensional unsteady heat conduction equation in the solid simultaneously with the first law in the gas phase, with an imposed heat transfer coefficient. Even at low compression ratios (of 2.5), notable effects of the solid walls are revealed, with thermodynamic cycle losses of up to 20% (relative to equivalent adiabatic and reversible processes) when unfavourable solid and gas materials are selected, and closer to 10-12% for more common material choices. The contribution of the solid towards these values, through the variations attributed to the thickness of the cylinder wall, is about 10% and 2-4%, respectively; showing a maximum at intermediate thicknesses. At higher compression ratios (of 6) a 19% worst case loss is reported for common materials. These results suggest strongly that, in designing high-efficiency reciprocating machines, the full conjugate and unsteady problem must be considered and that the role of the solid in determining performance cannot, in general, be neglected.