<p>This paper examines the thermal vibration and thermal buckling responses of functionally graded porous (FGP) beams considering temperature-dependent material properties. It focuses on three types of temperature distribution profiles, which are uniform, linear, and nonlinear profiles, across the beams' thickness. The study also considers four different porosity distribution schemes over the beams' cross-section. The governing equations of the FGP beam are derived using the principle of virtual work within the framework of the first-order shear deformation theory (FSDT). A mesh-free method utilizing <i>C</i>¹ Hermite point interpolation, in which Legendre polynomial basis functions are adopted for the first time, is employed to obtain the approximate solution. In addition, the analysis includes both axially movable and axially immovable boundary conditions. The convergence examples are performed, and the correctness of the study is confirmed. Influences of temperature change and temperature distributions, temperature-dependent and temperature-independent properties, porosity coefficient and porosity distribution schemes on the natural frequency and the critical buckling temperature of the FGP beams are numerically investigated and highlighted. The findings of this study provide significant insights for the research and engineering design of FGP beams subjected to thermal environments.</p>