Thermal post-buckling analysis of uniform slender and shear flexible columns with axially immovable ends is studied for various boundary conditions using a load-deflection curve (bifurcation diagram). Linear buckling load is computed as an eigenvalue problem and the location of initial perturbation in the non-linear analysis is chosen based on the linear eigenvector. Geometric non-linearity is considered using von-Karman strain displacement relations and load-displacement curves are established for the aforementioned boundary conditions. Elegant closed form solutions are obtained for the post-buckling load parameter to linear buckling load parameter as a function of amplitude ratio for the boundary conditions considered using least squares approximation. Numerical values obtained are in good agreement with available literature for the classical boundary conditions, and for the non-classical boundary conditions results are validated with the results obtained from the available FE formulation which is based...