A steady-state compressor relation can misattribute a lagged temperature response during load changes to a change in estimated efficiency. Motivated by the monitoring of near constant-speed, single-shaft gas turbines, this study evaluates a thermal inertia-inspired correction that couples one effective temperature state to an efficiency parameter through an extended Kalman filter (T-EKF). Controlled tests distinguish spurious efficiency excursions from imposed slow degradation. The original 18 cases are supplemented with 30 new noise realizations in each of six prescribed conditions, comparing seven methods over 60–600 s. Across these 180 additional realizations, the median efficiency root-mean-square error is 0.001658 for T-EKF, compared with 0.008402 for the steady-observation EKF and 0.005194 for causal smoothing. A same-structure unscented Kalman filter obtains nearly identical errors, whereas a three-state EKF with the known two-pole reference structure obtains a lower median error of 0.0007099. Time-constant and covariance sensitivity, thermodynamic parameter mismatch, and innovation diagnostics characterize the limits of the low-order approximation. Archived industrial records provide a separate temperature-output diagnostic, with a slight improvement in March and a slight deterioration in April, after parameter freezing. The approach provides a compact correction for dynamic mismatch under the tested assumptions; it does not demonstrate physical efficiency improvement or independently validated field efficiency accuracy.