Simultaneously developing three-dimensional laminar flow and heat transfer in the entrance region of trapezoidal channels have been investigated using numerical methods in the Reynolds number range from 10 to 1000. The principal and secondary velocity fields, the temperature field, and all associated heat and momentum exchange parameters have been examined. The present results for the fully developed flow region of the channels compare well with the available literature. In the entrance region, it is observed that the axial velocity profiles develop overshoots near the walls and particularly at the channel corners. It is shown that boundary-layer type of approximations, which lead to Reynolds-number-independent Poiseuille and Nusselt numbers, can be used for Reynolds numbers over 50 and after a few hydraulic diameters from the channel inlet. It is also shown that hydrodynamic entrance lengths calculated with methods based on fully developed flow data are grossly in error. New correlations are proposed for the entrance length, and for the friction and heat transfer coefficients.