The present work provides a reliable computational framework to investigate the laminar and turbulent forced convection of sodium and sodium–potassium (Na, NaK) in small-scale heat sinks with hydraulic diameters between 1 mm and 5 mm. Na and NaK flow and heat transfer are studied numerically for a wide range of Reynolds numbers from 600 to 9000 in three sharp-cornered miniature heat sinks with rectangular, pentagonal, and hexagonal cross sections. For a fixed surface area to volume ratio, it is observed that the rectangular minichannel heat sink provides the highest convective heat transfer rates. The rectangular miniature heat sink is shown to provide 280% higher convective heat transfer rates in comparison with the pentagonal heat sink. Moreover, the obtained convective heat transfer coefficients for NaK are almost 20% higher than the ones for Na in the investigated pentagonal heat sink. For the same flow Peclet number in the rectangular and hexagonal heat sinks, both Na and NaK provide nearly identical average Nusselt numbers. However, NaK shows greater local and average Nusselt numbers compared to Na at the same Reynolds number.