The invention relates to a turbine blade or vane for a gas turbine, having a blade or vane root, which is successively adjoined by a platform region with a transversely running platform and then a blade or vane profile which is curved in the longitudinal direction, having a platform surface, which is provided at the platform and can be exposed to hot gas, and having at least one cavity, which is open on the root side, through which a coolant can flow and which extends through the blade or vane root and at least into the platform region and is surrounded by an inner wall, the contour of which, running in the platform region, is set back with respect to the contour running in the blade or vane root, so as to form a recess. To provide a turbine blade or vane which has a service life which is extended with respect to fatigue while at the same time saving cooling air, the invention proposes that the recess, as a partial cavity, is set back so deep into the platform that it lies opposite the platform surface, forming an at least partially hollow platform, and that there is at least one means for diverting the coolant into the partial cavity.