A quadrupole method is developed to solve heat transfer through a periodic macro-contact with time varying constriction. The solution is based on Fourier developments of time periodic variables. The result shows that it is necessary to introduce the concept of "building-up" of constriction to explain the thermal behavior for short and moderate periods. It is demonstrated that three characteristic times govern the problem: contact period, characteristic time of the rod and "building-up" time of constriction. Simplified schemes of the apparent resistance are presented corresponding to three limiting states. The analytical approach is validated by a numerical solution.