The temperature distributions and heat transfer in the thermal entrance region, which results when a viscous, incompressible electrically conducting fluid flowing steadily in the presence of a transverse magnetic field between parallel electrically conducting walls, which are kept at a constant temperature up to a certain cross section, enters a region with a different wall temperature, are analyzed. Solutions have been obtained in terms of eigenfunctions and eigenvalues for two cases corresponding to a small value of the Peclet number and an infinite value. It is found that downstream temperature conditions do not have any effect upon the upstream temperatures to the left of the transition cross section when the Peclet number is large, whereas for a small Peclet number, this ceases to be so. Thermal entry lengths are seen to be diminished by the increase in conductivity conditions of the walls.