Direct numerical simulations (DNS) of turbulent flow and convective heat transfer in a square duct with axial rotation were carried out. The pressure-driven flow is assumed to be hydrodynamically and thermally fully developed, for which the Reynolds number based on the friction velocity and hydraulic diameter is kept at constant (Re-tau = 400). In the finite length duct, two opposite walls are perfectly insulated and another two opposite walls are kept at constant but different temperatures. Four thermal boundary conditions were chosen in combination with axial rotation to study the effects of rotation and Grashof number on mean flow, turbulent quantities and momentum budget. The results show that thermal boundary conditions have significant effects on the topology of secondary flows, profiles of streamwise velocity, distribution of temperature and other turbulent statistic quantities but have marginal effects on the bulk-averaged quantities; Coriolis force affects the statistical results very slightly because it exerts on the plane normal to main flow direction and the rotation rate is low; Buoyancy effects on the turbulent flow and heat transfer increase with the increase of Grashof number (Gr), and become the major mechanism of the development of secondary flow, turbulence increase, and momentum and energy transport at high Grashof number. (C) 2010 Published by Elsevier Ltd.