A door-type thrust reverser device for a turbojet engine nacelle is provided that includes a fixed structure, a mobile structure mobile with respect to said fixed structure, and at least one door mounted with the ability to pivot via pivots between a retracted position corresponding to the nacelle operating in direct-jet mode, and a deployed position corresponding to the nacelle operating in reverser-jet mode. The thrust reverser device includes a device for bleeding off some of a secondary or bypass airflow, which device is able to bleed off part of the secondary airflow from a duct through which the secondary airflow circulates and for conveying said bled-off airflow toward at least one pivot of the door, so as to cool areas on and/or around the door pivots.