A hydraulic circuit (1) associated with an internal combustion engine (M) and comprising a main cooling circuit (2) of the engine (M) provided with a circulation pump (4) for a cooling fluid, characterized in that the pump (4) is a rotary volumetric pump driven by the engine (M) with a fixed transmission ratio and generating, at least during a warm-up transient of the engine (M), a flow rate greater than that required for the cooling of the engine (M) and by comprising an auxiliary circuit (3) branched from the main circuit and selectively connectable thereto by valve means (20), said valve means (20) being configured for sending to said auxiliary circuit (3), at least during said warm-up transient of the engine (M), at least a fraction of the flow rate of the cooling fluid pumped by the pump (4), said auxiliary circuit (3) comprising at least a first heat exchanger (21) wherein the cooling fluid absorbs thermal energy from a first fluid (23;
- 26) at a higher temperature, and at least a second heat exchanger (22) wherein the cooling fluid transfers thermal energy to a second fluid (24) at lower temperature.