An analytical formulation is developed to predict transient heat conduction in a semi-infinite medium with a vertical finite line heat source, which represents a buried tower of a power transmission line foundation. Unlike past studies with a constant line heat source, the current model develops a time-dependent variable heating strength, as well as a time varying surface temperature of the ground. An approximate VHS model (variable heating strength) is developed for sinusoidal variations of the line source strength and surface temperature, in order to simulate seasonal variations of ground temperatures. The VHS model reduces computational time and exhibits good accuracy, when compared against a full exact solution. The model is applied to heat conduction in a tower foundation, with time-varying ground surface temperatures. Effects of ground thermal conductivity and diffusivity, as well as variations of the line source strength, are investigated in this article.