Immiscible injection of slug(s) into a microchannel with square blocks attached to the bottom surface of the channel is studied using the phase-field approach for interface tracking. It is confirmed that immiscible injection enhances heat transfer by up to 85% compared to miscible injection considering identical thermophysical properties. The differences in the rate of heat removal between immiscible and miscible injection are explained by the hydrodynamics of the system. It is also found that larger injected slug size does not necessarily result in greater heat removal and causes the average Nusselt number to behave non-monotonically, reaching an optimum value at a specific slug length. This non-monotonic trend has been explained by analyzing the hydrodynamics of the system. The effect of the inter-block distance generally showed a monotonic increasing trend for the average Nusselt number, except for a single slug length. This behavior has been explained by the vorticity and Fourier transform analysis. An alternating slug injection configuration has also been analyzed. The analysis of this configuration reveals a non-monotonic behavior of the average Nusselt number vs the number of injected slugs. This non-monotonic behavior shows that for each value of the selected slug length, there is a critical number of slugs, and consequently, a critical slug length for which the average Nusselt number reaches a maximum. The hydrodynamics of the system justifies this non-monotonic behavior. Finally, the friction factor and performance evaluation criterion are presented as a guideline for the design of the microchannels based on flow configuration.