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This paper discusses a method of measuring the instantaneous exhaust gas temperature by thermocouples. Measuring the exhaust gas temperature is useful for a better understanding of engine processes. Thermocouples do not measure the instantaneous exhaust gas temperature because of their limited dynamic response. A thermocouple compensation technique has been developed to estimate the time constant in situ. This method has been commissioned in a simulation study and a controlled experiment with a reference temperature. The studies have shown that the signal bandwidth has to be restricted, since noise will be amplified in the temperature reconstruction. The technique has been successfully applied to some engine exhaust measurements. A comparison between two independent pairs of thermocouples has shown that temperature variations at frequencies up to 80Hz can be recovered.