The present disclosure provides a cooling device for a turbo engine of an aircraft nacelle, including: a heat exchanger and an air outlet pipe. The nacelle includes a front housing that has a front lip forming a hollow leading edge that delimits an annular de-icing chamber. In particular, the cooling device further includes a pipe for supplying pressurized air that extends from an inlet end linked to a pressurized air source, to an outlet end forming an air ejection nozzle opening into the de-icing chamber, and the outlet pipe of the heat exchanger has an air outlet section that is arranged in the de-icing chamber in a position designed such that the pressurized air ejection nozzle forms an air suction pump in the outlet pipe of the exchanger.