The study of conductive-convective heat transfer for a flat plate with an internal heat source 1-4, generally makes use of dedicated differential equations or differential equations systems. To solve the operational calculation, integral transformations can be introduced. This creates an advantage in solving the equations and differential systems in the sense that they are reduced to solving some equations or systems of algebraic equations, which are, at least in theory, easier to solve. The conductive-convective heat transfer phenomenon involves the use of independent and time-dependent variables (t < 0). The Laplace transform introduces an alternative method in solving the differential equations and systems that describe this phenomenon. The purpose of the present analysis is to determine the temperature variation within the flat plate as a function of time and the position inside the plate for the said heat transfer, T(x,y,t). The presented case analysis considers a heat conducting plate in a three-dimensional Euclidean space5-8, but for simplification, only the displacement along the y direction will be used. The analysis of the temperature field propagation within the plate is done convective, with heat release to the environment. For the Finite Element Analysis (FEA) of the heat transfer model, the plate is meshed on the x, y coordinates and the resulting data used as input to a Matlab model.