The method of fractional time steps and splitting of operators has been used to obtain a numerical solution to the problem of transient heat transfer in a three-dimensional, anisotropic, composite rectangular slab. Heat transfer is coupled with thermal expansion, the latter changing the shape and size of the composite slab. The composite slab could be a laminated composite or may consist of several layered slabs bonded together. The bonding could be perfect or imperfect. Numerical results have been presented for the moving boundaries and transient temperatures for two bonded, layered slabs. With some minor changes, any number of bonded, layered slabs can be considered, and their volume fractions can be varied as desired.