This chapter is devoted to the study of transient heat conduction. The most elementary transient conduction problem is the case of a lumped system in which the internal resistance to heat conduction is negligible compared to the external convective resistance. An important dimensionless number is the Biot number defined by the ratio between internal and external thermal resistances. A lumped system approach is valid for a low Biot number, more specifically for \(Bi<0.1\) . Next, the solution to the one-dimensional transient heat conduction equation is developed for a semi-infinite solid. In this case, three boundary conditions are studied at the exposed face, namely, (a) constant temperature, (b) constant heat flux, and (c) heat convection, which result in analytical solutions based on a similarity variable. For plate, cylinder, and sphere geometries exposed to heat convection, the solutions of transient conduction follow Heisler's diagrams. Finally, the chapter analyzes the finite difference method applied to the transient problems.