A turbomachine component (e.g., a blade, vane, or any other suitable component) is defined at least partially in a radial direction and an axial direction orthogonal to the radial direction and includes a body defining an outer surface configured to be in thermal communication with a gas path flow in the axial direction. The component includes a thermal regulation channel system defined within the body which includes at least one radial channel configured to allow thermal regulation flow in the radial direction, and at least one axial channel configured to allow thermal regulation flow in the axial direction.