An annular wall of an aeronautical turbine engine, the annular wall having an axis and comprising an aerodynamic surface extending axially along the axis and circumferentially about the axis, the aerodynamic surface being configured to radially delimit a gas passage, the annular wall having a concavity extending radially from the aerodynamic surface, the annular wall being provided with a heat exchanger comprising a heat exchanger matrix and an aerodynamic profile, a heat transfer fluid circuit extending at least into the heat exchanger matrix, the heat exchanger matrix having a first portion housed in the concavity and a second portion extending radially outside the concavity and projecting radially from the aerodynamic surface, the aerodynamic profile having a leading edge and a trailing edge, the aerodynamic profile being fixed to the second portion of the heat exchanger matrix such that the leading edge and the trailing edge extend circumferentially and that the leading edge is radially spaced from the aerodynamic surface and outside the concavity, wherein the heat exchanger comprises at least one fin extending radially from the aerodynamic profile, opposite the heat exchanger matrix, and axially along the aerodynamic profile, the heat transfer fluid circuit extending within the aerodynamic profile.