The present study is one of first attempts to closed-form solutions of the thermoelastic stability problem of functionally graded (FG) conical shells subjected to the thermal loading within the first-order shear deformation theory (FSDT). The material properties of FG truncated conical shells vary continuously in the thickness direction. The governing thermoelastic stability equations of FG truncated conical shells under thermal loadings within the FSDT using Donnell shell theory have been derived and for freely supported boundary conditions are reduced to a set of linear algebraic equations using the Galerkin's method. The expressions for critical temperature differences of freely supported FGM truncated conical shells based on the FSDT subjected to the uniformly and linearly distributed temperatures across the thickness are obtained by solving the linear algebraic equations. The appropriate formulas for FG cylindrical shells based on the SDT are found, as a special case. In order to assure the accuracy of the results, present study are compared and validated with the known data available via literature. Finally, some parametric studies are conducted to investigate the influences of the shear stresses, volume fraction index, FG profiles and the conical shell characteristics on the critical temperature differences are discussed in detail. (C) 2016 Elsevier Ltd. All rights reserved.