Solar radiation is the main driving force for the energy source of solar collectors, and its intensity determines the amount of energy that solar collectors can absorb. Therefore, the periodicity of radiation intensity will lead to periodic fluctuations in the outlet water temperature of solar collectors. This study numerically investigates the effects of the heat source period, amplitude, inlet flow rate, and steady state heat source temperature on the thermal storage performance of conical spiral shell-tube energy storage systems when the inlet temperature varies periodically as a cosine function using fluent software. The results show that when heat source periods are between 5 and 300 min, compared to the constant heat source, the total energy storage capacity can be increased by a maximum of 7.32%. The melting time can be shortened by a maximum of 16.31%. The average energy storage rate and energy storage efficiency can be increased by a maximum of 4.08% and 0.17%, respectively. When amplitudes are increased from 0 to 20 K, the melting time, total energy storage capacity, and energy storage efficiency are reduced by 30.21%, 1.19%, and 1.64%, respectively. The average energy storage rate increases by 41.59%. Furthermore, compared to the constant heat source, increasing the inlet flow rate and steady state heat source temperature has more significant effects on the thermal storage performance under cosine wave heat sources. The results can provide some reference for the optimization of phase change thermal storage systems under unsteady state conditions.