A cooling grate of a cooler apparatus for cooling down a high-temperature granular conveyed material with cooling air while conveying the high-temperature granular conveyed material, the cooling grate comprising: a plurality of support members that support the granular conveyed material via a dead layer, the dead layer being formed by a granular buried material deposited on upper surfaces of the plurality of support members, the granular buried material having a lower temperature than a temperature of the granular conveyed material, the plurality of support members being arranged in a predetermined direction at intervals such that the slits are formed therebetween, the slits allowing the cooling air to pass therethrough, the cooling air being supplied to the granular conveyed material through the dead layer; and a plurality of covering members, each of which covers an entirety of a corresponding one of the slits from above, wherein each of the plurality of support members includes placement portions, such that the placement portions of the plurality of support members extend along the entire slits and are positioned at both sides of the slits in the predetermined direction, and the covering members are placed on the placement portions, and each of the plurality of covering members includes a tapered portion whose cross section is tapered upward, characterized in that each covering member is placed on the placement portions in a state where spacers are interposed between the tapered portion and the placement portions, the spacers are arranged at intervals in an orthogonal direction orthogonal to the predetermined direction, each of the plurality of support members includes flange portions protruding upward, upper ends of the respective flange portions serve as the placement portions, the spacers are arranged on the tapered portion of each covering member, and each covering member is placed on the placement portions in a state where the spacers are in contact with upper end edges of the placement portions. a plurality of support members that support the granular conveyed material via a dead layer, the dead layer being formed by a granular buried material deposited on upper surfaces of the plurality of support members, the granular buried material having a lower temperature than a temperature of the granular conveyed material, the plurality of support members being arranged in a predetermined direction at intervals such that the slits are formed therebetween, the slits allowing the cooling air to pass therethrough, the cooling air being supplied to the granular conveyed material through the dead layer; and a plurality of covering members, each of which covers an entirety of a corresponding one of the slits from above, wherein each of the plurality of support members includes placement portions, such that the placement portions of the plurality of support members extend along the entire slits and are positioned at both sides of the slits in the predetermined direction, and the covering members are placed on the placement portions, and each of the plurality of covering members includes a tapered portion whose cross section is tapered upward, characterized in that each covering member is placed on the placement portions in a state where spacers are interposed between the tapered portion and the placement portions, the spacers are arranged at intervals in an orthogonal direction orthogonal to the predetermined direction, each of the plurality of support members includes flange portions protruding upward, upper ends of the respective flange portions serve as the placement portions, the spacers are arranged on the tapered portion of each covering member, and each covering member is placed on the placement portions in a state where the spacers are in contact with upper end edges of the placement portions.