**7. Conclusions**

Both methods of transient fluid temperature measurement presented in the chapter can be used online.

The first method, in which a mathematical model of the thermometer is first-order differential equation, is the most suitable for thermometers with very small time constants. In such cases, the delay of thermometer indication is small compared to changes in fluid temperature. In turn, the industrial thermometers, which are designed to measure the temperature of the fluid of high pressure, are characterised by a considerable delay of indications in reference to the actual changes of fluid temperature. For such thermometers, the second-order thermometer model, allowing for modelling the signal delay, is more adequate [14].

The method described in this chapter is the most suitable for measuring the transient temperature of gases, such as air or exhaust gases. This is due to the fact that the time constant depends on the heat transfer coefficient on the outer surface of the thermometer and in turn on the Reynolds and Prandtl numbers. For gases such as air or exhaust gas, Prandtl number varies slightly in a wide range of temperatures. However, during measurement of the transient steam temperature, the value of Prandtl number varies significantly depending on the pressure and temperature [23]. In this case, the inverse marching method described in [24] is more appropriate for correction of the dynamic error.
