A cooling or heating fluid circulation system of the double-supported centrifugal pump, comprises a left shaft sleeve and a right shaft sleeve which are sleeved on the periphery of the pump shaft, a first left sealing gland and a second left sealing gland are sleeved on the periphery of the left shaft sleeve via a left outside stationary sealing ring, a left outside rotating sealing ring and a left inside stationary sealing ring respectively, a first right sealing gland and a second right sealing gland are sleeved on the periphery of the right shaft sleeve via a right outside stationary sealing ring, a right outside rotating sealing ring and a right inside stationary sealing ring respectively; a heat exchange fluid circulation channel, which is formed among the first left sealing gland, the second left sealing gland, the left shaft sleeve, the pump shaft, the right shaft sleeve, the first right sealing gland and the second right sealing gland, is connected with an external heat exchanger via an external channel; the heat exchange fluid therein is capable of rotating simultaneously with the rotating part and flowing along the axial direction of rotating part. The present invention is capable of directly cooling or heating the rotating parts which are most in need of cooling or heating, thus the temperature of the rotating parts can be kept in a certain range.