A combustor heat shield for a gas turbine engine has a heat shield panel adapted to be mounted to an inner surface of a combustor shell with a back face of the panel spaced-apart from the combustor shell to define an air gap therewith. Studs project from the back face of the panel for engagement in corresponding mounting holes defined in the combustor shell. Each stud has a threaded distal end portion for engagement with a nut outside of the combustor shell. At least one of the studs has a channel defined in a peripheral surface thereof. The channel extends longitudinally along the stud from an inlet end connectable to a source of cooling air outside of the combustor shell to an outlet end disposed within the air gap for locally providing cooling air at the base of the stud.