In this paper, the sensitivity of randomness in material parameters on the thermal buckling of conical shells embedded with and without piezoelectric layer is examined. A higher order shear deformation theory is used to model the system behaviour of the conical shell. The lamina material properties are modelled as basic random variables. A deterministic finite element method in conjunction with the first-order perturbation technique is employed to handle the randomness in the material properties. Typical numerical results for the second order statistics of the linear thermal buckling load of the composite conical shells/panels with and without piezoelectric layer are obtained. Mean value results are validated with those available in the literature and standard deviation results are also validated with an independent Monte Carlo simulation.