A cooled turbine vane for a turbine engine, that includes a blade mounted on a platform carried by a base, the blade including one or more cavities formed therein for cooling air circulation, the cavity extending along the trailing edge and being supplied with cooling air by a supply duct connecting an air intake located in a lower portion of the base and the cavity of the trailing edge by defining a bend within the base. The duct includes, on an axis substantially radial relative to the air intake a bell-shaped niche located under the platform, the niche being open at a top thereof via a dusting hole extending through the platform and being defined at a foot of the base by walls extending substantially radially from the platform to close the platform laterally.