<p>Functionally graded graphene origami-enabled auxetic metamaterials (FG-GOEAM) have attracted much attention due to their excellent negative Poisson’s ratio properties. Research on the vibration characteristics of FG-GOEAM cylindrical shells remains insufficient. To fill this gap, this work systematically investigates the free vibration behavior of FG-GOEAM cylindrical shells under different temperature profiles using first-order shear deformation shell theory. There are three common types of temperature profiles: uniform temperature rise, linear temperature rise, and sinusoidal temperature rise. Temperature correction functions for LTP and STP conditions are established by taking the geometrically neutral surface temperature of each layer of the shell as a proxy for the overall temperature of that layer. To accurately characterize the effects of thermal effects, a thermal strain energy analysis model is introduced in this work. The material parameters were determined based on a micromechanical model assisted by genetic programming. The governing equations are derived by Hamilton’s principle and solved by Navier’s method. After validating the model, this work investigates the effects of key parameters on the vibration characteristics of the FG-GOEAM cylindrical shell. The numerical results of this work are expected to provide a theoretical basis for the structural optimization and innovative design of FG-GOEAM cylindrical shells.</p>