Summary: Investigated are the initial stages of laminar two-dimensional thermal-fluid forced and mixed convective heat transfer from flow accelerated past an elliptic cylinder. The cylinder is taken to be inclined at an angle with the horizontal, and the viscous incompressible Boussinesq fluid accelerates uniformly from rest past it. Two types of solutions are presented. The first type takes the form of an approximate analytical solution valid for small times and large Reynolds numbers. The second type is a numerical solution obtained by numerically integrating full Navier-Stokes and energy equations using a spectral-finite difference procedure.