Highly concentrated triple-junction solar cells (HCTJSCs) are cells that have diverse applications for power generation. Their electrical efficiency is almost 45%, which may be increased to 50% by the end of the year 2030. Despite their overwhelming ability to generate power, their efficiency is lower when utilized in a concentrated manner, which introduces a high-temperature surge, leading to a sudden drop in output power. In this study, the efficiency of a 10 mm × 10 mm multijunction solar cell (MJSC) was increased to almost 42% under the climatic conditions in Lahore, Pakistan. Active cooling was selected, where SiO2–water- and Al2O3–water-based nanofluids with varying volume fractions, ranging from 5% to 15% by volume, were used with a 0.001 kg/s mass flow rate. In addition, two- and three-layer microchannel heat sinks (MCHSs) with squared microchannels were designed to perform thermal management. Regarding the concentration ratio, 1500 suns were considered for 15 August at noon, with 805 W/m2 and 110 W/m2 direct and indirect radiation, respectively. A complete model including a triple-junction solar cell and allied assemblies was modeled in Solidworks software, followed by temperature profile generation in steady-state thermal analyses (SSTA). Thereafter, a coupling of SSTA and Ansys Fluent was made, in combination with the thermal management of the entire model, where the temperature of the TJSC was found to be 991 °C without active cooling, resulting in a decrease in electrical output. At 0.001 kg/s, the optimum average surface temperature (44.5 °C), electrical efficiency (41.97%), and temperature uniformity (16.47 °C) were achieved in the of MJSC with SiO2–water nanofluid with three layers of MCHS at a 15% volume fraction. Furthermore, the average outlet temperature of the Al2O3–water nanofluid at all volume fractions was high, between 29.53 °C and 31.83 °C, using the two-layer configuration. For the three-layer arrangement, the input and output temperatures of the working fluid were found to be the same at 25 °C.