There is an increasing request in energy recovery systems that are more efficient, environmentally friendly and economical. The free piston Stirling engine has been investigated due to its structural simplicity and high efficiency, coupled with its cogeneration ability. This study presents the numerical investigation of quasi-steady model of a gamma type free piston Stirling engine (FPSE), including the thermodynamic analysis of the heat exchangers. Advanced thermodynamic models are employed to derive the initial set of operational parameters of the FPSE due to the coupling of the piston’s (displacer and piston) dynamics and the working process. The proximity effect of the heater and cooler on the regenerator effectiveness in relation to the heat losses, output power, net work and thermal efficiency of the FPSE are also observed and presented in this study. It can be observed that at temperatures of 541.3 °C and 49.8 °C of the heater and cooler, respectively, with heater volume of 0.004 m3, regenerator volume of 0.003 m3 and cooler volume of 0.005 m3, the FPSE produced an output performance of 996.7 W with a thermal efficiency of 23% at a frequency of 30 Hz. This approach can be employed to design effective high performance FPSE due to their complexity and also predict a satisfactory performance.