TD learning and its refinements are powerful tools for approximating the solution to dynamic programming problems. However, the techniques provide the approximate solution only within a prescribed finite-dimensional function class. Thus, the question that always arises is how should the function class be chosen? The goal of this paper is to propose an approach for TD learning based on choosing the function class using the solutions to associated fluid and diffusion approximations. In order to illustrate this new approach, the paper focuses on an application to dynamic speed scaling for power management.