An upgrade method for a gas turbine comprising: a compressor that compresses air supplied through an air supply line; a combustor that is supplied with fuel and combusts compressed air compressed by the compressor; a turbine that is rotated by combustion gas generated by the combustor; a cooling air supply part that supplies part of the compressed air to the turbine as cooling air for the turbine; an air intake valve that is provided in the air supply line and adjusts an amount of air supplied to the compressor; and a control system that calculates an opening degree set value of the air intake valve relative to a measured output value that is a measurement result of a gas turbine output, on the basis of the measured output value and a first function defining a relation between the measured output value and the opening degree set value; adjusts an opening degree of the air intake valve on the basis of the calculated opening degree set value; and obtains a set temperature that is preset for exhaust gas discharged from the turbine, relative to a pressure ratio of the compressor, on the basis of the pressure ratio and a second function defining a relation between the pressure ratio and the set temperature, the upgrade method comprising upgrading the gas turbine by: making settings so that the supply amount of the cooling air supplied to the turbine is reduced, and replacing at least some of components provided in the turbine with components that can be cooled with the reduced supplied amount of cooling air; changing the first function according to the post-upgrade supply amount of cooling air and the replaced components; and changing the second function to a function that is calculated from a first correction value and a second correction value, the first correction value corresponding to a further decrease in an exhaust gas temperature due to thermal expansion caused by a rise in the post-upgrade pressure ratio, the second correction value corresponding to a further rise in the exhaust gas temperature caused by a decrease in the supply amount of cooling air. a compressor that compresses air supplied through an air supply line; a combustor that is supplied with fuel and combusts compressed air compressed by the compressor; a turbine that is rotated by combustion gas generated by the combustor; a cooling air supply part that supplies part of the compressed air to the turbine as cooling air for the turbine; an air intake valve that is provided in the air supply line and adjusts an amount of air supplied to the compressor; and a control system that calculates an opening degree set value of the air intake valve relative to a measured output value that is a measurement result of a gas turbine output, on the basis of the measured output value and a first function defining a relation between the measured output value and the opening degree set value; adjusts an opening degree of the air intake valve on the basis of the calculated opening degree set value; and obtains a set temperature that is preset for exhaust gas discharged from the turbine, relative to a pressure ratio of the compressor, on the basis of the pressure ratio and a second function defining a relation between the pressure ratio and the set temperature, the upgrade method comprising upgrading the gas turbine by: making settings so that the supply amount of the cooling air supplied to the turbine is reduced, and replacing at least some of components provided in the turbine with components that can be cooled with the reduced supplied amount of cooling air; making settings so that the supply amount of the cooling air supplied to the turbine is reduced, and replacing at least some of components provided in the turbine with components that can be cooled with the reduced supplied amount of cooling air; changing the first function according to the post-upgrade supply amount of cooling air and the replaced components; and changing the second function to a function that is calculated from a first correction value and a second correction value, the first correction value corresponding to a further decrease in an exhaust gas temperature due to thermal expansion caused by a rise in the post-upgrade pressure ratio, the second correction value corresponding to a further rise in the exhaust gas temperature caused by a decrease in the supply amount of cooling air.