In this study, the flow dynamics and heat transfer in partially filled pin-based microchannel heat sinks (MCHS) are examined. The lattice Boltzmann method is used to analyse the physics of these systems and examine the effects of the flow, pin configuration, size and porous medium height. The results of the study reveal that, unlike the fully filled pin-based MCHS, there is no unique behaviour for the pin configuration effects and the performance of partially filled pin-based MCHS depends on the porous medium size and structure as well as the inertial forces in the flow. In particular, it is found that there are hydrodynamic and thermal-based critical porous medium heights at which the best performance in terms of heat removal switches from the inline to the staggered configuration. The dependence of these critical heights on the Reynolds number and the porous medium properties are analysed and the effects of the flow dynamics are further unravelled through a particle tracing technique. Furthermore, a simple flow model is developed, and is shown to capture well the main trends obtained from the simulations and to bring to light more of the system physics that help explain the interplay between the different parameters.