A gas turbine with a sequential combustor arrangement as disclosed includes a first combustor with a first burner for admitting a first fuel into a combustor inlet gas during operation and a first combustion chamber for burning the first fuel, a dilution gas admixer for admixing a dilution gas to the first combustor combustion products leaving the first combustion chamber, a second burner for admixing a second fuel and a second combustion chamber. To assure a temperature profile after the dilution gas admixer and to increase the gas turbine's power and efficiency a vane and/or blade of the turbine has a closed loop cooling. The outlet of the closed loop cooling is connected to the dilution gas admixer for admixing the heated cooling gas leaving the vane and/or blade into the first combustor combustion products.