Abstract Buckling and postbuckling behavior of carbon nanotube‐reinforced composite (CNTRC) cylindrical shells with tangentially restrained edges exposed to preexisting temperature conditions and subjected to uniform external pressure are presented in this analytical study. Three temperature conditions considered are that uniform temperature rise, through‐the‐thickness temperature gradient, and in‐plane linear temperature distribution. Carbon nanotubes (CNTs) are reinforced into matrix phase through uniform or functionally graded distributions. The properties of CNTs and matrix are assumed to be temperature‐dependent and effective moduli of CNTRC are determined according to extended rule of mixture. Governing equations are based on the classical shell theory taking into account Von Karman‐Donnell nonlinearity and elasticity of tangential constraints of edges. Multi‐term solutions of deflection and stress function are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to derive closed‐form expression of nonlinear pressure‐deflection relation from which critical buckling pressures and postbuckling paths are determined. A variety of numerical examples are given and interesting remarks are achieved. Due to practical situations of boundary edges and various temperature conditions, this paper aims to analyze separate and combined influences of tangential edge constraints and preexisting temperatures on thermomechanical postbuckling behavior of pressure‐loaded nanocomposite cylindrical shells.