Systems, program products, and methods for detecting thermal stability within gas turbine systems are disclosed. The systems may include a computing device(s) in communication with a gas turbine system, and a plurality of sensors positioned within or adjacent the gas turbine system. The sensor(s) may measure operational characteristics of the gas turbine system. The computing device(s) may be configured to detect thermal stability within the gas turbine system by performing processes including calculating a lag output for each of the plurality of measured operational characteristics. The calculated lag output may be based on a difference between a calculated lag for the measured operational characteristics and the measured operational characteristic itself. The calculated lag output may be also be based on a time constant for the measured operational characteristics. The computing device(s) may also determine when each of the calculated lag outputs are below a predetermined threshold.