Features and methods for modulating a flow of cooling fluid to gas turbine engine components are provided. In one embodiment, an airfoil is provided having a flow modulation insert for modulating a flow of cooling fluid received in a cavity of a body of the airfoil. In another embodiment, a shroud is provided comprising a cooling channel for a flow of cooling fluid and an insert that varies in position to modulate the flow of cooling fluid through the cooling channel. In yet another embodiment, a method for operating a gas turbine engine having a cooling circuit for cooling one or more components of the gas turbine engine comprises increasing power provided to the engine and decreasing power provided to the engine to modulate a position of a flow modulation insert located in the cooling circuit and thereby modulate the flow of cooling fluid through the cooling circuit.