Abstract: A guide vane arranged in an air flow from a fan of an twin-spool aircraft engine, the aerodynamic part of the vane including an internal lubricant cooling passage partly delimited by an extrados wall and an extrados wall of the vane. The passage is equipped with a heat conduction matrix compressed between the walls and separating a first lubricant circulation space from a second lubricant circulation space. Furthermore, the matrix defines firstly first contact elements of the intrados wall formed in the first space and between which the lubricant from the first space will circulate, and secondly second contact elements of the extrados wall formed in the second space and between which the lubricant from the first space will circulate.