Thermal load acting on a beam, which is fixed at its both ends to restrict its thermal expansion generates axial pressure and reduces the vibration frequencies of bending vibration.Thermal buckling happens if the temperature is high enough.Changing the distribution of the beam cross sections can change the axial pressure, thus improve fundamental frequency and critical thermal temperature.In this paper, beam under thermal load for maximum fundamental frequency and critical thermal buckling temperature is optimized with given volume constraint.Size optimization of the beam cross sections is studied.Single and bimodal optimum designs for maximum frequency and maximum critical thermal temperature are obtained depending on the lower bound on cross section.Numerical experiments show that optimum frequency increased more significantly under thermal load.With increasing thermal load, the optimum solution of frequency design is similar to the solution of maximum critical thermal buckling temperature design;the optimum solution of critical thermal buckling design is similar to the solution of maximum critical force design.To explain these phenomena, optimum design of the beam cross sections of minimum axial pressure is studied.Its multiple optimum designs with bang-bang type cross sectional area distribution is notable.