In order to understand the heat transfer performances of the liquid metal with low melting point compared with conventional coolants, the heat transfer performances of laminar flow in a circular duct with constant wall heat flux using liquid gallium and water as coolants were theoretically analyzed by considering the influence of thermally developing region, and the effect on heat dissipation was evaluated by using the mean wall temperature. The results indicate that when duct length(Z,) or Re remains constant, the critical Re(Re,c) and critical length($Xc$) exist respectively, the cooling effect of liquid gallium is better than that of water only when the $Re>Re,c$ or $L<LC$. It is found that the critical Re increases linear with duct length and the critical length increases linear with Re. It is also found that increasing Re or lessening the duct length can make the cooling superiority of liquid gallium over water more prominent. All the results provide the theoretical base for better designing the cooling systems that use liquid metal as coolant.