This paper presents an analytical approach to investigate the buckling of sandwich cylindrical shells subjected to uniform temperature rise and external lateral pressure. Two sandwich models corresponding to carbon nanotube reinforced composite (CNTRC) face sheets and core layer are considered. The properties of all constitutive materials are assumed to be temperature dependent and effective properties of CNTRC are determined according to an extended rule of mixture. Governing equations are established using first order shear deformation theory and solved employing two-term form of deflection along with Galerkin method for simply supported edge shells. In order to account for practical situations of in-plane boundary condition, the elasticity of tangential constraint of boundary edges is included. Owing to temperature dependence of material properties, critical thermal loads are determined adopting an iteration process. Numerous parametric studies are carried out and interesting remarks are given. The study reveals that sandwich shell model with CNTRC core layer and homogeneous skins has considerably strong capacity of buckling resistance. Numerical results also indicate that tangential edge constraint has significant effects on critical loads, especially at elevated temperature. In addition, in the case of thermal load, an intermediate volume percentage of carbon nanotubes can confer the highest critical temperatures of sandwich shells.