A wide range of applicability of the Reynolds analogy between turbulent momentum and heat transport implies inherent difficulty in diminishing or enhancing skin friction and heat transfer independently. In the present study, we introduce suboptimal control theory for achieving a dissimilar control of enhancing heat transfer, while keeping the skin friction not increased considerably in a fully developed channel flow. The Fréchet differentials clearly show that the responses of velocity and temperature fields to wall blowing/suction are quite different, due to the fact that the velocity is a divergence-free vector field while the temperature is a conservative scalar field. This essential difference allows us to achieve dissimilar control even in flows where the averaged momentum and energy transport equations have an identical form. It is also found that the resultant optimized mode of control input exhibits a streamwise travelling-wave-like property. By exploring the phase relationship between the travelling-wave-like control input and the velocity and thermal fields, we reveal that such control input contributes to dissimilar heat transfer enhancement via two different mechanisms, i.e. direct modification of the coherent components of the Reynolds shear stress and the turbulent heat flux, and indirect effects on the incoherent components, through modification of the mean velocity and temperature profiles. Based on these results, a simple open-loop strategy for dissimilar control is proposed and assessed.