A novel thermal storage solar air heater (TSSAH) is proposed in this study. This TSSAH is composed of a vacuum glass tube, flat micro-heat pipe arrays (FMHPA), and a thermal storage material (i.e., paraffin) with a phase change temperature of 58 °C. The FMHPA acts as the core heat transfer component. Considering the low heat conductivity coefficient of paraffin, louver fins are utilized to enhance heat transfer. Thermal performance is analyzed and discussed. During thermal collection, natural convection evidently contributes to enhancing heat transfer. Increasing solar radiation intensity can improve collection efficiency. Thermal collection efficiency increases from 70.22% to 77.28% when solar radiation is increased from 675 W/m2 to 835 W/m2 under an ambient temperature range of 20.8 °C–23.3 °C. A high ambient temperature results in high collection efficiency that can reach 80.59%. During thermal discharge, enhancing the air volumetric flow rate can evidently increase the amount of useful energy and shorten discharge time. From 80 m3/h to 170 m3/h, the amount of useful energy is increased from 335 W to 550 W, and discharge time is shortened from 309 min to 195 min under inlet temperatures ranging from 24.1 °C to 24.2 °C. A high inlet temperature generates a high outlet temperature but decreases the amount of useful energy. From 19.7 °C to 32.0 °C, outlet temperature is increased from 30.4 °C to 36.6 °C, and the amount of useful energy is reduced from 692 W to 287 W at an air volumetric flow rate of 200 m3/h. During thermal discharge, the average amount of useful energy can reach 692 W at an inlet temperature of 19.7 °C and an air volumetric flow rate of 200 m3/h, indicating that the proposed TSSAH can release heat quickly. In the experiment scale, the discharged heat is 6150–6450 kJ at a phase change material temperature scale of 85 °C–35 °C.