Abstract: The external heat flux of low Earth orbit (LEO) cuboid-shaped satellites varies significantly due to the complex spatial relationships among the satellite, Earth, and Sun. Conventional computational methods are often inefficient and lack intuitive visual representation. Transformation relationships among the geocentric inertial (GCI), primary/secondary orbital (PORF/SORF), and satellite body coordinate systems were established. The Sun vector trajectory was dynamically modeled in GeoGebra, and its projection on satellite surfaces was analyzed over a full orbital period. This approach enabled rapid evaluation of solar radiation, Earth’s infrared radiation, and Earth albedo heat flux. Compared to conventional numerical methods, the proposed method demonstrated superior computational efficiency and enhanced physical interpretability. Validation through high-fidelity Thermal Desktop (TD) simulations confirmed its accuracy, demonstrating its applicability in early-stage thermal control design and optimization for satellite constellations.