A twofold thin shell theory and HSDT was differently applied by [PERSON] et al. [42] to study the nonlinear buckling response of FG porous GPL-reinforced cylindrical shells. [PERSON] et al. [43] comprehensively investigated the static, free, and forced vibration of FG porous annular sector plates reinforced by GPLs, based on a FSDT, while applying a Rayleigh-Ritz energy formulation and finite element approach to determine and solve the governing equations of motion, respectively. Moreover, [PERSON] and [PERSON] [44] proposed a third-order shear deformation theory (TSDT) and mesh-free method to solve the stability problem of FG porous smart sandwich structures reinforced with graphene nanocomposite layers. [PERSON] [45] applied successfully an isogeometric approach based on a non-uniform rational B-splines (NURBS) for the study of FG-GPL porous nanocomposite plates via a refined plate theory. Different plate theories were also proposed in Ref. [46] to investigate the wave propagation in FG porous plates reinforced with GPLs, whose governing equations of the problem were derived by means of the Hamilton's principle. Based on the available literature, however, a limited attention has been paid, up to date, on the thermal stress analysis of FG-GPL structures. Only in the recent work by [PERSON] et al. [47], an analytical solution was proposed by the authors to analyze the thermal buckling and forced vibration of porous GPL-reinforced nanocomposite cylindrical shells, based on a modified couple stress theory. Refs. [48; 49] also focused on the thermo-mechanical vibration of FG curved nanobeams and truncated cones with porosities and reinforced by GPLs, even in a nonlocal sense. A static behavior of rotating truncated conical shells under thermo-mechanical loads was studied by [PERSON] et al. [50], based on a FSDT. Accordingly, [PERSON] and [PERSON] [51] investigated the nonlinear thermomechanical vibration of FG annular plates/disks subjected to a non-uniform thermomechanical loading condition in a dynamic sense, by applying a 3D thermoviscoelasticity theory. A hygro-thermo-mechanical nonlinear study was also proposed recently for curved thin and moderately thick shallow FG panels in [52]. [PERSON] et al. [53] presented a semi-analytical solution for FG rotating disks by enforcing both Dirichlet and Neumann boundary conditions while implementing a homotopy perturbation method (HPM) for a thermomechanical loading condition. A similar problem was also studied by [PERSON] et al. [54] to check for the critical buckling behavior of stiffened rotating FG cylindrical shells subjected to a thermomechanical loading, as provided by a FSDT and DQM. More recently, a 1D finite element method has been proposed in [55] to investigate the 3D thermoplastic response of rotating disks with variable thickness by employing a Carrera-unified formulation (CUF). [PERSON] and [PERSON] [56] studied the response of rotating FG hybrid cylindrical shells with a piezoelectric layer under hygothermal conditions. [PERSON] [57] applied a general theoretical framework to survey the dynamics of rotating doubly-curved shell structures made of FG materials. [PERSON] and [PERSON] [58] optimized the weight of a rotating FG annular disk with variable thickness subjected to a thermo-mechanical loading by using co-evolutionary particle swarm optimization and DQMs. Based on the available literature, in most cases the investigations focus on the steady state and time dependent thermal stresses of cylindrical shells, where a little attention is given to the thermoelastic behavior of conical shells under a transient thermal loading. Starting with the preliminary work [59], the present work provides a more generalized investigation on the transient thermal stress behavior of FG rotating cones in presence of possible porosities. The multilayer cone is assumed to be reinforced with uniform and non-uniform GPLs in a metallic matrix with possible open-cell internal pores.