The aim of this work is to improve theoretical and experimental tools for modelling and characterising the global behaviour of measurement microphones in a large range of environmental conditions. In most of measurement microphones, the sensitive part is a vibrating membrane stretched and clamped on the body of the microphone. If the sensor is operated at ambient temperatures that significantly differ from atmospheric one, thermal expansion of the microphone membrane and body causes strain and stress variations in the membrane, which lead to altered vibrational behaviour when it is submitted to an acoustic wave. An analytical approach is developed here to express the thermal stress related to the fact that thermal expansions of the microphone membrane and body are different. These effects are then taken into account in a classical modelling procedure for describing the vibration of a microphone membrane in vacuo. An experiment, that relies on the electrostatic actuator technique, has been performed in a fine vacuum to characterise the first resonance mode of a commercial microphone membrane in low temperatures range, from atmospheric to cryogenic. The experimental results highlight the significant effects of the thermal stress induced by the differences between thermal expansion properties of the materials constituting the microphone. These results are consistent with the membrane vibration predicted by the analytical modelling proposed. Thus, even small differences between the thermal expansion properties of the microphone membrane and body have to be taken into account in a modelling procedure to get reliable predictions of the membrane vibration at various ambient temperatures.