Clear-sky conditions are an essential need to allow proper high-temperature solar cooking. Moreover, it is not an easy task to accomplish evening cooking, especially during wintertime when solar radiation is available only for a few hours. A solution to bypass these drawbacks lies in adopting a cooker provided with a thermal storage unit. The storage unit proposed in this work is a double-walled vessel composed by two stainless steel cylindrical pots assembled concentrically. The annular space between the pots was loaded with 4 kg of phase change material (PCM) based on a ternary mixture of nitrite and nitrate salts (solar salt: 53 wt% KNO3, 40 wt% NaNO2, 7 wt% NaNO3). The thermal storage unit was characterized by means of a test rig including a high-concentration-ratio (10.78) solar box cooker. Four different sets of 14 experimental tests, divided into a heating and a cooling phase, were carried out to assess the performance of the solar cooker with the storage unit. It was found that the PCM thermal storage significantly improves the load thermal stabilization when solar radiation is not available: the load cooling time in the range 170-130 degrees C was determined to be from 65.12% to 107.98% higher than that without the solar-salt-based PCM thermal storage, proving the effectiveness of the proposed solution.