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This work is to investigate thermal buckling of an automotive brake disc. Plate theories, including von Karman plate equations, are studied and applied to derive and formulate thermal buckling problems. Analytical solutions using Timoshenko beam theory and the Rayleigh-Ritz methods to formulate and study an annular disc are developed. A numerical method, Finite Element Analysis (FEA), is applied and compared with the analytical results to validate FEA methods for buckling studies. The FEA method and procedure are applied for a parametric study to quantify the effects of disc thickness, loading pattern, boundary constraint, as well as the rotor hub section height, on thermal buckling loads and modes for a brake rotor disc. It is found that thermal buckling of a brake rotor performs differently from an annular disc. The annular disc in general can not be used to predict brake rotor disc buckling performances. The boundary condition and rotor hub section height factors play important roles in determining thermal loads and modes. Under normal operation conditions, the brake rotor should not buckle due to the induced thermal load alone. In addition, a brake rotor disc buckling is sensitive to geometry imperfection but an annular disc is not.