Brake force distribution is a pivotal aspect of vehicular safety and performance, profoundly impacting the heat generation and dissipation within drum brake systems. This research investigates the intricate relationship between brake force distribution ratio (β) and the heat flux experienced by drum brakes during variable braking events. The present research is motivated to find an appropriate β and thereby employs computational modeling to elucidate the multifaceted effects of force distribution on the thermal behavior of hydraulic drum brakes. Respective design parameters are chosen to optimize the hydraulic brake design components using multi-objective evolutionary algorithm (MOEA). An optimal β of 0.686 is determined, which splits the brake forces appropriately between the front and rear axles to obtain a balanced heat flux of 1.98 W/mm2. Such insights are invaluable for designing safer and more efficient braking systems, with inferences on the vehicle braking performance, longevity, and overall road safety.