Thermal contact resistance under general time-dependent thermal load is investigated in this study. Assuming known number of contacts points, and the average surface area of each contact, the focus of this study is on the thermal aspect of contact resistance, i.e. spreading/constriction resistance at the contact point. A general analytical solution for thermal spreading/constriction resistances of a time-dependent circular source on a finite circular cylinder with uniform side and end cooling is presented. The solution is applicable to a general axisymmetric heat flux distribution, including both isoflux and isothermal distributions. The time response of the flux tube under different geometrical and boundary conditions is investigated and the result are shown. The results are also compared to, and successfully verified by an independent numerical simulation.