The study of heat transfer in the entrance region of ducts with different cross-sections is important in engineering practice. This paper considers laminar, hydrodynamically fully developed flow in the thermal entrance regions of rectangular passages, emphasizing heat transfer aspects. By having a prescribed heating or cooling rate and considering the wall temperature to depend on the axial coordinate alone, the temperature solution leads to an integral equation. Solution of this equation is found using an inverse technique to determine the temperature at the walls. For verification purposes, an asymptotic solution is developed which produces results that agree very well with those from the inverse analysis. The results include a correlation and computed values of the Nusselt number at entrance locations, for rectangular ducts with different aspect ratios. (C) 2007 Elsevier Ltd. All rights reserved.