Exhaust gas temperature (EGT) is a key parameter in diagnosing the health of gas turbine engines (GTEs). In this article, we propose a model-driven spectroscopic network with strong generalizability to monitor the EGT rapidly and accurately. The proposed network relies on data obtained from a well-proven temperature measurement technique, i.e., wavelength modulation spectroscopy (WMS), with the novelty of introducing an underlying physical absorption model and building a hybrid dataset from simulation and experiment. This hybrid model-driven (HMD) network enables strong noise resistance of the neural network against real-world experimental data. The proposed network is assessed by in situ measurements of EGT on an aero-GTE at millisecond-level temporal response. Experimental results indicate that the proposed network substantially outperforms previous neural-network methods in terms of accuracy and precision of the measured EGT when the GTE is steadily loaded.