A three-dimensional mathematical model of a narrow copper plate coupled with the cooling water is established to elucidate the heat transfer and cooling intensity in a small chamfered slab mold with original and redesigned schemes. Then, the precision of the models is validated by measured temperatures of the copper plate in actual production. The water boxes, bolts and thermocouple holes are considered, and the temperature distribution on different longitudinal and transverse planes is discussed. A novel one-hole and one-slot cooling structure is proposed for a small chamfered narrow copper plate. The results show that the Redesign1 scheme with an 8 mm diameter round hole makes the maximum temperature decrease from 673.5 to 644.0 K, reduced by 29.5 K. By analysing temperature uniformity on the hot face at maximum temperature transverse plane and second-row bolts transverse plane, it is found that the standard deviation value in Redesign1 decreases 8 to 10 K, compared with the Original scheme. Besides, it is seen from the Redesign1# scheme that while the water velocity of the round hole water slot can be controlled to be 9.24, 11.24 and 13.24 m s−1, the maximum values of copper plate temperature are reduced to 616.4, 606.9 and 599.3 K, respectively. Compared with the Original scheme values, the maximum temperature difference is 74.2 K. Hence, the cooling uniformity of the chamfered copper plate should be improved by increasing the water velocity of the round hole water slot.