Innovative design of microchannel heat sinks (MCHS) remains a contemporary research need to meet the increasing cooling demand of modern electronic industries. A transient three-dimensional conjugate heat transfer study has been carried out here for different combinations of constrictors like ribs or protrusions along with cavities on the sidewalls of a microchannel (MC). A facing pair of cavities with circular arc sections, together called a fan-shaped cavity (FC), has been considered. Each in the facing pair of ribs (R) or protrusions (P) is in the form of a part of cylinder or sphere, respectively. The results include the variations of Nusselt number, friction factor, and thermal performance over a range of Reynolds numbers from 140 to 605 in microchannels with rib (MCR), protrusion (MCP), or cavity pairs alone (MCFC), as well as with cavity-rib pairs (MCFCR) or cavity–protrusion pairs (MCFCP). Contrasting the highest thermal performance of 1.6 reported in an earlier study on MCFCR, a value as high as 1.76 has been obtained around Re of 550 for MCFCP with the relative values of cavity length, width, and pitch of 0.015, 0.5, and 0.0625, respectively, along with protrusion length and width of 0.01 and 0.4, respectively. The mechanisms leading to spiraling transverse streamlines in both MCFCR and MCFCP have been explained. The superior performance of MCFCP has presumably arisen from the vortex structure with no interference with the boundary layers at the top and bottom walls.