This article presents analytical solutions to initial boundary value problems of thermoelasticity with a priori unknown evolving boundaries. To be more precise, we consider a spherical shell of arbitrary thickness subjected to the internal and external pressures of corrosive media at generally different temperatures, with taking into account the mechanochemical effect and inhibition of corrosion process. Conditions under which the circumferential stress can serve as the equivalent stress are determined. It was found that the life of the shell was influenced by the competing effects of the pressures and temperatures on the corrosion rate and stress values, as well as by possible moving the location of the maximal stress. It was also concluded that the elastic stress component played a decisive role in the synergistic growth of the total thermoelastic stress and the corrosion rate.