This paper is investigating the transient solution for a heat conduction problem in solids with insulated boundary. This class of problem is often encountered in automotive brake and clutch systems where the frictional heat generated at contact surface is much larger than that the system is capable of dissipating. The heat conduction equation can be solved through the superposition of the homogenous solution and the particular solution. The use of the steady state solution as a particular solution can however result in a lack of numerical accuracy because of its order of magnitude driven by the nearly insulated boundary. A special solution form is proposed for the particular solution to account for such boundary condition. The proposed solution was tested in the context of a typical clutch disk sliding between two non-conductive rigid bodies. The solution has proven to be time efficient and free of numerical accuracy associated with the order of magnitude of the particular solution.