A kit for changing during maintenance or reengineering the cooling schema of a blade forming part of a stage of a gas turbine; the kit comprising a blade provided with: an airfoil profiled section having a pressure side and a suction side joined together at chordally opposite leading and trailing edges; at least one cooling passageway extending between the pressure side and the suction side along the leading edge, the at least one cooling passageway configured for enabling cooling fluid to flow therefrom; a plurality of film holes extending between the at least one cooling passageway and an exterior of the airfoil profiled section, the plurality of film holes being configured for directing at least a portion of the cooling fluid from the at least one cooling passageway to flow over a portion of the airfoil profiled section; an insert operably disposed within the at least one cooling passageway, the insert being selectively operable to close the plurality of film holes, in order to interrupt the flow of the cooling fluid over a portion of the airfoil profiled section and direct the flow of the cooling fluid to flow from the leading edge to the trailing edges within the airfoil profiled section, and to open the plurality of film holes, in order to enable the flow of the cooling fluid over the portion of the airfoil profiled section to form the film cooling layer extending from the leading edge to the trailing edge, the kit moreover comprising: a covering bend configured to be secured over the at least one cooling passageway to enable at least a portion of the cooling fluid to flow from the leading edge to the trailing edges within an interior portion the airfoil profiled section, when the plurality of film holes are closed by the insert; a flat covering member with an orifice, configured to be secured over the at least one cooling passageway to enable the cooling fluid from the orifice to flow within the at least one cooling passageway, which is to be directed from the plurality of film holes, from the leading edge to the trailing edges when the plurality of film holes are opened by the insert in order to form a film cooling layer extending from the leading edge to the trailing edge. an airfoil profiled section having a pressure side and a suction side joined together at chordally opposite leading and trailing edges; at least one cooling passageway extending between the pressure side and the suction side along the leading edge, the at least one cooling passageway configured for enabling cooling fluid to flow therefrom; a plurality of film holes extending between the at least one cooling passageway and an exterior of the airfoil profiled section, the plurality of film holes being configured for directing at least a portion of the cooling fluid from the at least one cooling passageway to flow over a portion of the airfoil profiled section; an insert operably disposed within the at least one cooling passageway, the insert being selectively operable to close the plurality of film holes, in order to interrupt the flow of the cooling fluid over a portion of the airfoil profiled section and direct the flow of the cooling fluid to flow from the leading edge to the trailing edges within the airfoil profiled section, and to open the plurality of film holes, in order to enable the flow of the cooling fluid over the portion of the airfoil profiled section to form the film cooling layer extending from the leading edge to the trailing edge, a covering bend configured to be secured over the at least one cooling passageway to enable at least a portion of the cooling fluid to flow from the leading edge to the trailing edges within an interior portion the airfoil profiled section, when the plurality of film holes are closed by the insert; a flat covering member with an orifice, configured to be secured over the at least one cooling passageway to enable the cooling fluid from the orifice to flow within the at least one cooling passageway, which is to be directed from the plurality of film holes, from the leading edge to the trailing edges when the plurality of film holes are opened by the insert in order to form a film cooling layer extending from the leading edge to the trailing edge.