In high average power laser system, electro-optic switches encounter both limitation of aperture and thermo-effects. Plasma-electrodes technology is adopted to scale the switch to large aperture, and thin KD*P is used as electro-optic crystal to reduce absorption of the laser. Based on analyzing themo-effects, a mean of end-face conduction-cooling the KD*P is arised, and optimum design is done. Numerical simulation results show that, by adopting one piece of sapphire to cool two pieces of KD*P, the required switch-voltage could be reducd to 27 kV. For 35 W/cm2 average power density laser, the maximum depolarization in the end-face conduction-cooled switch, which has a 40 mm×40 mm aperture, is 0.22%, and the peak to valley(PV) value is 0.60 λ. These perturbations are acceptable to meet the design requirements.