Passive thermal management in electronics has disadvantages of low efficiency and high cost. Herein, experimental and numerical studies on the geometric optimization of a hygroscopic‐membrane heat sink (HMHS) are conducted. The HMHS is based on water evaporation from a membrane‐encapsulated hygroscopic salt solution, in which pin fins are used for thermal conductivity enhancement. A comprehensive heat and mass transfer model is developed and validated. To obtain the HMHS configuration with the maximum cooling performance, an approach that couples the Taguchi method with numerical simulations is utilized. The contribution ratio of each design factor is determined. Experimentally validated results demonstrate that the maximum temperature reduction provided by the HMHS can be further improved from 15.5°C to 17.8°C after optimization, achieving a temperature reduction of up to 21°C at a fixed heat flux of 25 kW/m2 when compared with a similarly sized fin heat sink. Remarkably, the optimized HMHS extends the effective cooling time by ∼343% compared with traditional phase‐change materials, achieving a maximum temperature reduction ranging from 7.0°C to 20.4°C. Meanwhile, the effective heat transfer coefficient achieved is comparable with that of forced liquid cooling. Our findings suggest that the proposed cooling approach provides a new pathway for intermittent thermal management, which is expected to be used for thermal regulation of electronics, batteries, photovoltaic panels, and LED lights.