This investigation is devoted to evaluating the thermal hydraulics behavior of sodium-based (Na) miniature heat sinks. The investigated geometrical parameters cover a range of 0.143–1 for heat sink aspect ratios, 0.267–21.7 mm for hydraulic diameters, and 600–20,000 for the Reynolds number. As the first objective in this work, two correlations are developed and proposed for Na friction factors and average Nusselt numbers in steel (SS-316) miniature heat sinks with a hydraulic diameter of less than 5 mm. Obtained correlations for Nusselt numbers and friction factors estimate the numerical results with a margin of error of 5% and 10%, respectively. The developed correlation for the average Nusselt number in Na-cooled miniature heat sinks is compared against available and reported correlations in the literature for macroscale liquid metal-cooled pipes and channels. It is revealed that the available correlations in the literature tend to significantly overestimate the Nusselt number in rectangular miniature heat sinks with a hydraulic diameter of less than 5 mm. As the second objective in this work, the developed and verified numerical model is utilized to evaluate the thermal efficiency of Na-cooled copper-based miniature heat sinks with an innovative design that includes a corrosion-resistant coating (cladding layer). The thickness of the corrosion-resistant coating varies from 0.25 mm to 4.5 mm with a thermal conductivity range of 4–17 (W/m K). The cladded heat sink aspect ratio and its hydraulic diameter vary between 0.29–1 and 2500–10,000, respectively. Two different trends are observed for the thermal efficiency of the protective cladding layer in terms of its thermal conductivity. In this class of small-scale heat sinks with the employed aspect of 0.29, a considerable thermal efficiency enhancement of the corrosion-resistant coating is obtained by increasing its thermal conductivity. However, in cladded miniature heat sinks with aspect ratios of 0.635 and 1, the thermal efficiency of the cladding layer tends to decrease as its thermal conductivity increases. A maximum of 30% enhancement in the thermal efficiency of the investigated cladded copper-based miniature heat sinks is observed compared to identical miniature heat sinks made totally out of the cladding layer material. The obtained results reveal that the copper-based cladded miniature heat sink of aspect ratio 1 provides the highest thermal efficiency among all the three investigated cladded heat sinks.