An analytical/numerical method for solving the problem of non-stationary heat diffusion in multilayered slabs is presented. This is an extension of previous methods that have been used to solve transient heat diffusion problems in one-dimension. In this work, two-dimensional semi-infinite media are considered and double integral transforms are used to obtain the corresponding transfer matrix form from the governing partial differential equations. Numerical techniques are used to compute the overall transfer matrices of the system and to numerically invert them in order to obtain transient results. Difficulties encountered with the numerical operations and ways to circumvent these are presented. The developed methodology has been applied to two-layered configurations.