Most solar cookers usually perform a single task of solely cooking food during sunshine hours. Solar cookers coupled with thermal energy storage (TES) material for off-sunshine cooking are usually expensive and require complex engineering designs, and cannot be used for dual purposes, for example, solar water heating and cooking. In this paper, a solar cooker that can perform dual tasks of cooking as well as storing thermal energy to be used during off-sunshine periods is presented. The experimental setup is composed of a parabolic dish, a solar receiver coupled with a flat plate and an oil-circulating copper coil for charging and discharging a storage tank. The objective of the experiment is to evaluate the energy and exergy thermal performance parameters of the dual-purpose system during charging and discharging cycles. The effect of the flow rate and the mass of the load are investigated while using sunflower oil as both the heat transfer fluid and the storage material. Charging and discharging experiments are conducted using four different flow rates (2, 3, 4, 5 mL/s), and with different masses (0.5, 1, 1.5, 2.0 kg) with water and sunflower oil as the test loads. The charging results show that the average energy and exergy rates as well as their corresponding efficiencies increase with an increase in the charging flow rate. On the other hand, the increase in the mass load tends to decrease marginally the average charging energy and exergy rates for water, and their corresponding efficiencies. For sunflower oil, the average charging energy and exergy rates and efficiencies showed a more pronounced decrease with an increase in the mass. Water generally shows higher charging and discharging energy and exergy efficiencies compared to sunflower oil with an increase in the flow rate. For discharging results, the correlations between the energy and exergy thermal performance parameters with respect to the flow rate and the heating load are not well defined possibly due to different initial storage tank temperatures at the onset of discharging and the inefficient discharging process which needs to be optimized in future.