Nowadays, climate change and global warming phenomena are becoming more and more serious issues. In order to sustain the enormous worldwide energy demand, society consumes a high amount of fuel, resulting into the steep increase of the level of CO\textsubscript{2} in the environment. Therefore, the massive greenhouse gases emissions in the atmosphere, generated by burning fossil at a great pace, are the main reason behind the previously mentioned phenomena. Heat transfer augmentation methods can considerably contribute to the decrease of fuel consumption, resulting into a reduction of the greenhouse gases emissions. Therefore, this can be an effective approach to tackle the climate change and global warming phenomena. Particularly, rough surfaces are a well known heat transfer augmentation technique. Such surfaces induce turbulence and thereby the flow is well mixed. This mechanism assists convective heat transfer and as a result, heat transfer is augmented. In addition, buoyancy-influenced turbulent flows frequently occur in many engineering applications. These flows combine natural and forced convection which are due to buoyancy and the bulk flow respectively and contribute both to heat transfer. Particularly, buoyancy-aided flows can promote laminarization and therefore heat transfer deterioration. The main focus of this study is to examine the impact of surface roughness and buoyancy effects on turbulent heat transfer. Initially, a 3D rectangular channel is considered with the streamwise, wall normal and spanwise dimensions being 5.63 $\times$ 2 $\times$ 2.815. Subsequently, two different wall roughness geometries are constructed. Both of them have a sinusoidal shape, however the direction of travel is in the streamwise direction for the one and in the spanwise for the other. Moreover, the surface roughness is placed on the top and bottom isothermal walls of the geometry. Regarding the space and time discretization, central differences are used for the former one and second order Adams-Bashforth for the latter one. Finally, the immersed boundary method is utilized in order to incorporate the surface roughness. A series of direct numerical simulations is performed to gain an insight on how surface roughness and buoyancy forces affect the heat transfer. The results display that both roughness schemes enhance heat transfer. Particularly, the Reynolds stresses show an increase in both rough wall cases, signifying that mixing is improved. In addition, the turbulent heat flux as well as the Nusselt numbers also exhibit a growth for both streamwise and spanwise orientation, implying that heat transfer is augmented. Comparing the streamwise and spanwise orientations with each other, both Reynolds stresses and turbulent heat flux graphs are significantly higher in the streamwise roughness case. Moreover, the streamwise roughness is enhancing the Nusselt number approximately 1.8 times more than the spanwise roughness for the zero-buoyancy case and approximately 1.4 times more for the buoyancy-aided scenario. Noteworthy is the fact that, the results show that the buoyancy-aided case predicts larger Reynolds stresses, turbulent heat flux and Nusselt numbers for all of the surfaces.