By-pass transition and heat transfer in an initially laminar low Reynolds number channel flow with rough walls are investigated using direct numerical simulations. The aim is to determine whether or not the turbulence can be triggered and maintained under these circumstances. The roughness elements are square rod bars of large heights. Three-dimensional pseudo-turbulence cannot be triggered when the roughness elements extend the width of the channel. A staggered configuration is necessary to break up the spanwise symmetry, in which case a pseudo-fully developed rough regime sets up even at very low Reynolds numbers, leading to large Nusselt numbers over the crests. There is a dissimilarity between the fluctuating temperature and the velocity fields.