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We numerically evaluated the thermal performance of microchannel heat sinks, considering rectangular, hexagonal, and circular cross-sections. Moreover, as a passive heat transfer augmentation technique, dimples were added to improve the rectangular microchannel heat sinks. These simulations use nanofluids based on TiO2 nanoparticles or nanotubes dispersed in bidistilled water as working fluids. The mathematical model considered variable thermophysical properties of the nanofluids; for this purpose, polynomial fittings correlate the dependence of the thermophysical properties on the temperature. We considered a heat flux of q″ = 50 W/cm2 at the microchannel’s lower surface as a boundary condition along with laminar flow conditions. The numerical simulations allowed the Nusselt numbers and entropy generation calculation, which were the basis for the thermal performance calculation. Regarding the effect of TiO2 nanoparticles shape, spherical TiO2 nanoparticles based nanofluids using rectangular microchannels improve the Nusselt number. Moreover, the frictional entropy decreases with nanofluids based on TiO2 nanotubes, but the thermal entropy decreases with nanofluids based on TiO2 nanotubes. Incorporating dimples in the rectangular microchannel enhances the Nusselt numbers and lowers the entropy generation. Considering the Reynolds number range and from the perspective of Nusselt number and entropy generation, we concluded that the microchannels must be operated at a high Reynolds number to improve the microchannel heat sinks thermal performance.