A heat shield element arrangement including a heat shield element for a heat shield arranged on a supporting structure is provided. On each of the two opposing sides running parallel to the installation grooves the heat shield element includes a continuous screw head opening which penetrates the cold side and the hot side of the heat shield element substantially vertically and through which the screw head of the respective screw is arranged to be accessible to the supporting structure, and a spring element may be arranged under the respective screw, which spring element may be extended along the hot side of the heat shield element and the parallel installation groove of the supporting structure. An outer end of the spring element is embodied as a clamping retaining hook which is provided for the purpose of engaging in the laterally recessed retaining groove of the heat shield element.