A three-dimensional solid–fluid conjugate model is employed to provide physical insights into the effect of wall conduction on fluid convection in a diamond-shaped microchannel. The study covers the effect of divergence-convergence angle, width ratio, thermal conductivity ratio, thickness ratio, and Reynolds number on peripheral heat flux, temperature, and Nusselt number profiles. Isotherms show a multidirectional thermal gradient for low thermal conductivity ratios, whereas only an axial thermal gradient is seen for higher thermal conductivity ratios. Furthermore, the overall axial surface temperature gradients decrease with increasing divergence-convergence angle and decreasing width ratio. The study also shows that the thermal conductivity ratio significantly influences the Nusselt number, while the thickness ratio has only a moderate influence for all geometries. The analysis also reveals that at a particular intermediate thermal conductivity ratio, the Nusselt number becomes maximum. Lastly, a nondimensional wall conduction number is used to characterize conjugate effects in diamond microchannels. The wall conduction effect is inconsequential in diamond microchannels when the nondimensional wall conduction number is less than 0.01. The present study is beneficial from a practical perspective as it helps design the optimum channel geometries subjected to conjugate effects for many heat transfer applications.