Research is being actively conducted on the continuous thin plate casting method, which is used to manufacture magnesium alloy plate for plastic processing. This study applied a heat transfer solidification analysis method to the melt drag process. The heat transfer coefficient between the molten magnesium alloy metal and the roll in the thin plate manufacturing process using the melt drag method has not been clearly established until now, and the results were used to determine the temperature change. The estimated heat transfer coefficient for a roll speed of 30 m/min was 1.33 × 105 W/m2·K, which was very large compared to the heat transfer coefficient used in the solidification analysis of general aluminum castings. The heat transfer coefficient between the molten metal and the roll estimated in the range of the roll speed of 5 to 90 m/min was 1.42 × 105 to 8.95 × 104 W/m2·K. The cooling rate was calculated using a method based on the results of deriving the temperature change of the molten metal and the roll, using the estimated heat transfer coefficient. The DAS was estimated from the relationship between the cooling rate and DAS, and compared with the experimental value. When the magnesium alloy is manufactured by the melt drag method, the cooling rate of the thin plate is in the range of about 1.4 × 103 to 1.0 × 104 K/s.