A composition with a kinematic viscosity for cooling and lubricating a drive system of an electric or hybrid vehicle, measured at 100 C. in accordance with the standard ASTM D445, in the range 3 to 10 mm.sup.2/s. The composition includes 70% to 90% of a base oil or a mixture of base oils having a kinematic viscosity, measured at 100 C. in accordance with the standard ASTM D445, of 1.5 to 8 mm.sup.2/s and selected from polyalphaolefins; and at least one thickening polymer.