The conjugate cooling of a single block heater mounted on a conductive wall of a parallel plates channel was investigated under distinct laminar airflow constraints: fixed flow rate, fixed channel flow pressure drop and fixed pumping power. The heater was cooled by direct forced convection to the airflow and by conduction through its contact with the channel wall. The investigation was performed for a two-dimensional configuration with fixed channel geometry and variable heater height. At the channel entrance the flow velocity and temperature were uniform. The channel wall thickness was constant and its thermal conductivity ranged from 0 to 80 that of the air, while the heater thermal conductivity was equal to 500 that of the air. The conservation equations were solved numerically by the control volumes method with the SIMPLE algorithm. The results were expressed in dimensionless form, considering the three distinct flow constraints. For a fixed flow rate, the heater temperature always decreased as the heater height increased.For the other two flow constraints, there is a critical relative heater height which minimizes its thermal resistance to the airflow. The results also indicated that for a conductive substrate, the conduction from the heater to the substrate plate cannot be neglected in comparison to the direct convective cooling to the airflow.