The thermal modeling and analysis of a transparent insulation materials (TIM) covered solar integrated collector storage (ICS) water heating system with phase-change material (PCM) is carried out in this paper The system consists of a double rectangular enclosure of cross section 1 m x 1 m where the top enclosure is filled with paraffin wax and that of the bottom is with water. The transient response of the PCM-water solar ICS system is studied with and without fins on the diurnal basis. The performance of the system is investigated with 4, 9, and 19 fins inside the wax having a pitch of 20 cm, 10 cm, and 5 cm, respectively. The latent heat storage with nine fins is found to be optimum for maximum water temperature and minimum heat losses to the surroundings. The temperature of water in the ICS exceeds 50 degrees C with a temperature drop of only 1.5-2 degrees C during nighttime. The nine-fin solar ICS configuration attains similar to 9 degrees C higher than other configurations.