Thermal management and temperature control of the electrical, electronic, and electrochemical devices during their operation have always been a challenge for proper performance and further development of them. In this regard, the utilization of liquid-cooled mini-channel heat sinks (MCHSs) and improving their capability for heat dissipation have been considered an effective method in past decades. The current study aims to improve the hydrothermal performance and temperature uniformity of MCHS. To this end, several channel configurations with novel geometrical cross sections, namely basic case and cases 1–4, are designed to investigate the influence of geometrical parameters on the mini-channel performance and temperature distribution inside the heat sink. Moreover, the hydrothermal improvement of each model in comparison to the basic case is computed through a parameter, namely performance evaluation criteria (PEC). Additionally, the impact of employing water-based ternary hybrid nanofluid (THNF) containing TiO2-MgO-GO ternary hybrid nanoparticles (THNPs) with various volume fractions and shape factors (SFs) instead of distilled water in the mini-channel with optimized hydrothermal behavior is thoroughly scrutinized. the outcomes endorse that in case 3 with trapezoidal geometry and PEC parameter equal to 1.2, the Nusselt number improves by 3.2 and 1.3 times, in comparison to case 2 (lowest values of Nusselt number) and base case, at Reynolds number of 831. Also, this is observed that hydraulic diameter directly impacts the pressure drop, and by decrement of that, the pressure drop heightens. However, case 2 with a rhombus geometry results in better temperature uniformity due to its larger effective heat transfer area. Furthermore, it is observed that the volume fraction and SF of THNP significantly affect the hydrothermal behavior of THNF inside the MCHS. For instance, by employing THNF with volume fractions of 0.03 % and 0.05 %, the average heat transfer coefficient (HTC) improves by 9 % and 17 %, pressure drop increases by 220 Pa and 370 Pa, and thermal resistance reduces by 9 % and 25 %, respectively, at Reynolds number of 1496, compared to distilled water. Further, THNF with a volume fraction of 0.05 %, reduces the maximum temperature of the heat sink by 3 K in comparison to distilled water, at a Reynolds number of 831. In addition, the utilization of disparate types of THNP with various SF, including spherical (sf = 3), platelets (sf = 5.7), blades (sf = 8.6), and lamina (sf = 16.1576) is examined and disclosed with volume fraction of 0.05 % and SF of 16.1576 instead of 3, HTC roughly elevates by 67 % and thermal resistance decreases by 47 %, at a Reynolds number of 831.