Thermal-lag engines (TLE) are external combustion engines with a single piston that offer the potential for reduced maintenance and production costs compared to traditional Stirling engines. Despite these promising prospects, studies on the physical behavior of this engine type remain limited. In this study, three novelties are presented: (1) a novel computational fluid dynamics-mechanism dynamics (CFDMD) model with high complexity for the TLE; (2) an analysis of the work generation in relation to the phase difference between pressure and volume; and (3) an analysis of the thermal-lag phenomenon based on the full spectrum of the phase difference between temperatures and piston position. In the CFDMD model, there are two key components: a computational fluid dynamics (CFD) model that captures the temporal evolution of the three-dimensional thermo-fluid fields and a mechanism dynamics model that solves the transient dynamics of the crank-drive mechanism. The CFDMD model effectively simulates the complex interplay between the thermodynamic behavior of the working gas and the dynamic behavior of the engine mechanism. The study additionally investigates the temporal evolution of the engine speed and examines its dynamic behavior. The influence of parameters, including crank radius, heating temperature, and initial crank angle, on shaft power and brake thermal efficiency is thoroughly explored. To gain a profound understanding of the indicated work generation mechanism and the thermal-lag phenomenon, the discrete Fourier transform provides full spectra of the periodic quantities of interest generated by the CFDMD model. It is found that the numerical average engine speed at different heating temperatures and torques from the CFDMD model is in good agreement with the experimental data, with a maximum difference of 140 rpm. The shaft power decreases from 19.8 to 5.3 W, while brake thermal efficiency increases from 4.5 to 7.7% as the initial crank angle varies from −90° to 90°. The first-oscillation phase differences between pressure and volume are close to 180°, decrease as the heating capacity is raised, and dominate the swelling of the PV diagrams. Only the first harmonic oscillation of the heater temperature exhibits the thermal-lag phenomenon.