The Mark II free-piston heat actuated heat pump (HAHP) utilizes a linear magnetic coupling to transfer engine power across a hermetic shell, thereby driving the refrigerant compressor piston. Compliance in the coupling affects the dynamic behavior of the system. This paper presents the results of dynamic/thermodynamic analyses performed on a baseline Mark II design that is intended for the residential heat pump market. The machine has 3 ton cooling capacity at 95°F ambient conditions. Load matching behavior is evaluated using the HFAST Stirling cycle thermodynamics code, coupled to harmonic equations representing the 5 degree-of-freedom free-piston dynamic system. Behavior at outdoor ambients from 115°F to 0°F is presented, along with the results of nonlinear transient simulations done to verify stability.