The laminar, incompressible, hydrodynamically fully developed and thermally developed and developing flow is studied in straight elliptic ducts with aspect ratio a* varying from 0.25 to 0.99 (which is an almost circular duct). The duct wall is subjected successively to constant temperature, to circumferential uniform and axially linearly or exponentially varying temperature. Numerical results obtained with the ADI scheme indicate that the friction factor increases as aspect ratio a* decreases. In the thermally developing flow a high Nusselt number decreases as a* decreases. In the thermally developed limit as a* decreases, the Nusselt number increases for small axial wall temperature distributions, while decreases for large axial wall temperature values.