Heat dissipation of high-power lasers needs a cold storage and supply system to provide sufficient cooling power. A compact coil-plate heat exchange device has been proposed and applied in the phase-change cold storage system with ice as the cold-storage medium and glycol aqueous solution as the coolant. The heat exchanger consists of several stacked coil-plate units and each unit is constructed with a flat plate and serpentine coils welded on the plate. A simulation model on the cold achieving process of a coil-plate unit was built and verified by the corresponding experiment. The influences of the structural parameters (tube diameter, tube pitch, and plate spacing) of the unit and the inlet temperature and volume flow rate of the coolant on the heat exchange power density were analyzed to obtain the maximal cooling effect in a limited time period. It was found that the heat exchange power density is limited when the tube pitch and plate spacing are large, otherwise, the effective cooling time period is limited. A small plate spacing can make the power density decrease rapidly in the later stage. The inlet coolant temperature can significantly affect the heat exchange power density while the coolant volume flow rate in tube has a small effect on the power density when the coolant is in turbulent state. In a time period of 900 s, for a coil-plate heat exchanger with a plate size of 940 mm ×770 mm and a tube pitch of 78 mm, when the plate spacing is 20 mm, the average heat exchange power density is 5.1 kW/m2 when the inlet temperature and volume flow rate of the coolant are 20 °C and 0.5 m3/h, respectively. The total cooling power of several stacked coil-plate units in the limited time period can match the high requirement of laser heat dissipation.