A cold storage unit can store the cold energy off-peak and release it for building cooling on-peak, which can reduce the electricity load of air conditioning systems. N-tetradecane is a suitable cold storage material for air conditioning, with a phase change temperature of is 4–8 °C and a phase change enthalpy of 200 kJ/kg. However, its low thermal conductivity limits the application of n-Tetradecane for high-power cold storage/release. This paper prepares a tetradecane/expanded graphite (EG) composite phase change material (CPCM), whose thermal conductivity can be increased up to 21.0 W/m·K, nearly 100 times over the raw n-tetradecane. A novel model to predict the maximum loading fraction of paraffin in the EG matrix is presented, with an error within 1.7%. We also develop a thermal conductivity model to predict the thermal conductivity of the CPCM precisely, with an error of less than 10%. In addition, an innovative spiral wave plate cold storage tank has been designed for the tetradecane/EG composite. The power and energy density of the cold storage tank are significantly improved compared to that of raw tetradecane. The energy density reaches 40 kWh/m3, which is high among the organic PCM thermal storage tank. This paper shows the significance of thermal conductivity enhancement in designing a cold storage tank.