The response of composite columns under axial compressive loading, and in which a non-uniform temperature distribution through the thickness exists, is investigated. This non-uniform temperature distribution can develop when one side of the structures is exposed to heat flux. In this paper, we assume that this distribution is linear, which corresponds to a steady state temperature profile due to heat conduction. The degradation of the elastic properties with temperature (especially near the glass transition temperature of the matrix) is accounted for, by using experimental data for the elastic moduli. Furthermore, the formulation includes transverse shear and it is done first for the general non-linear case and subsequently linearized. Due to the non-uniform stiffness and the effect of the ensuing thermal moment, the structure behaves like an imperfect column, and responds by bending rather than buckling in the classical Euler (bifurcation) sense. Another important effect of the non-uniform temperature is that the neutral axis moves away from the centroid of the cross-section, resulting in another moment due to eccentric loading, which would tend to bend the structure away from the heat source. Simple equations for the response of the column are derived and results are presented for the variation of the deflection with the heat flux, as well as for the combined effects of the applied load and heat flux. It is found that the thermal moment would tend to bend the structure away from the heat source for small temperatures (small heat fluxes) but towards the heat source for large temperatures. On the contrary, the moment induced due to the eccentric loading would always tend to bend the structure away from the heat source. Results indicate the combined influences of these moments and that of axial constraint.