Installation of flat solar collectors (FSCs) has been increasing due to the zero cost of renewable energy. However, the performance of this equipment is limited by the area, the material and the thermophysical properties of the working fluid. To improve the properties of the fluid, metal and metal oxide nanoparticles have mainly been used. This paper presents the performance assessment of the FSCs using simple and hybrid carbon nanofluids of low thermal capacity. Energy and mass balance modeling was performed for this study. A parametric analysis was conducted to examine the impact of key variables on the performance of the solar collectors using simple graphite and fullerene nanofluids, as well as hybrid metal–oxide–carbon nanofluids. From the results of heat transfer in FSCs, using graphite and fullerene nanofluids, it can be concluded that adding these nanoparticles improves the convection coefficient by 40% and 30%, respectively, with 10% nanoparticles. The graphite and fullerene nanoparticles can enhance the efficiency of FSCs by 2% and 1.5% more than base fluid. As the decrease in efficiency using fullerene with magnesium oxide is less than 0.2%, fullerene hybrid nanofluids could still be used in FSCs.