Temperature- dependent surface tension gamma(1v)(T) and its temperature coefficient gamma'(1V)(T) [=d gamma(1V)(T)/dT] for liquid metals are thermodynamically determined on the basis of an established model for surface energy of crystals. The model predictions correspond to the available experimental or theoretical results. It is found that for metallic liquids gamma(1V)(Tm) proportional to H-v/V-m (2/3), gamma(1V)(T) proportional to T, and y'(1V) (T) - T over a certain temperature range (including T IV < T-m and T >= T-m), where H-v and V-m are the liquid-vapor transition enthalpy at boiling temperature T-b and the atomic volume at melting temperature T-m, respectively. Furthermore, T(m)gamma'(1V) (T-m)/gamma(1V)(T-m) almost remains IV constant, which gives a way to estimates of gamma'(1V)(T-m) values when T-m and gamma(1V)(T-m) are known.