To prevent deterioration of quality of fluid due to heating of bearing lubrication, in a pump which is an inner bearing type and performs self- lubrication by the transferred fluid.

Reflux passages P1, P2 are communicated with lubrication grooves 7M, 8M of bearings 7, 8 for flowing fluid lubricating the bearings back to a suctioning port D of a pump. Cooling jackets 9, 10 are arranged on the reflux passages P1, P2. Coolant is charged into and circulated through the jackets 9, 10. After the lubrication, the fluid is cooled through the reflux passages P1, P2 to the same temperature as the suctioning port D.