In mixed boundary value (MBV) problems, the nature of the boundary condition can change along a particular boundary (finite, semi-infinite or infinite in length), say from a Dirichlet condition to a Neumann condition. Most MBV problems are solved using classical techniques such as separation of variables (domain of limited extent) or transform methods (domain of semi-infinite or infinite extent) which lead to dual or triple integral equations. Also, they are usually solved when a steady state condition is reached [1]. In authors’ knowledge, the only exception is the paper by Sadhal about solids with partially contacting interface [2]. In this work we deal with both steady state and transient MBV problems which are solved as inverse heat conduction (IHC) problems [3] using Green’s functions [4] and superposition in space and time.