A cooling structure for a turbomachine. In one embodiment, the cooling structure is for a seal slot of the turbomachine. The cooling structure includes a body coupled to a surface of the seal slot. The body includes a passageway on a first surface of the body for providing a cooling fluid to the seal slot. In an other embodiment, a apparatus includes a first component and a second component adjacent the first component. The apparatus also includes a seal slot extending between the first component and the second component, and a cooling structure positioned within the seal slot. The cooling structure includes a body coupled to a surface of the seal slot. The body has a passageway on a first surface of the body for providing a cooling fluid to the seal slot.