Machine tools are an indispensable part of the modern manufacturing industry, by which many items are produced. In the manufacturing process, machining accuracy is very important for the precision of products. However, the thermal error accounts for 40–70% of the machining error. Most of the machine tool heat created during machining originates from the rotating spindle owing to the internal bearing friction and motor power loss. Cooling systems are designed to remove the heat generated in the spindle in real time by coolant circulation to maintain the spindle temperature and improve the machining accuracy of the machine tool. In this study, the thermal deformation of a spindle was investigated under different rotating spindle speeds. To adapt to cooling demand variations at different rotating speeds, the cooling capacity of the cooling system was controlled by changing the supply volume and supply temperature of the coolant to the spindle. The effects of supply coolant volume, supply coolant temperature, and ambient temperature on the thermal deformation of the spindle were analyzed. A regression model for the driving frequency of the coolant pump in terms of the spindle rotational speed and coolant temperature difference was developed. By changing the supply coolant volume and coolant temperature difference in accordance with the spindle rotating speed, the accuracy of the deformation was reduced by up to 25%, and the required time to attain a steady state was also shortened. The shortest required time of 12 min was attained with a pump driving frequency of 80 Hz and a coolant temperature difference of 4 °C at a spindle rotating speed of 24000 rpm. The developed regression model was verified in three dynamical operational processes with different periods in which the spindle rotating speed was changed.