Based on dependences that describe the nonstationary temperature fields in the membrane and casing of the tensoresistive pressure sensor, we derived equations for thermomechanical processes in these elements, specifically equations of thermal deformation and thermal stresses. These equations make it possible to explore the effect of a thermal deflection in the membrane, as well as thermal stresses and thermal deformations in it, on the static and dynamic characteristics of the sensor. It is shown that the combination of thermal elastic processes in the membrane under a fast-changing effect of temperature on it significantly distorts the static and dynamic characteristics. It was established that during thermal deflection relative deformations on the surface of the membrane can be commensurate with the working deformations during pressure measurement, while a transitional characteristic of the sensor may differ from normal by up to 60 %. Our research shows that it is possible, when enabling radial thermal deformation, synchronized with the membrane of the sensor's casing, in the region of coupling with the membrane, to minimize thermal stresses in it. In addition, by minimizing the heat transfer along the perimeter of the sensor's membrane it is possible to eliminate the gradient of a temperature field along the radius. This is the way to minimize a thermal deflection of the membrane and decrease a temperature error of the sensor. Employing such measures may substantially reduce the influence of a fast-changing temperature on metrological characteristics of the sensor.