Ultralight heat-dissipating materials are essential for the effective thermal management of mobile devices. Graphene aerogel is a highly porous material made of thermally conductive carbon nanomaterial. Owing to aerogel's highly porous structure and graphene's high intrinsic thermal conductivity, graphene aerogel has a very low density and could be a promising ultralight thermal management material. In this study, forced convective heat transfer inside graphene aerogel is experimentally examined, and the effect of the aerogel microstructure on the heat and fluid flow characteristics of the graphene aerogel is discussed. It is established that graphene aerogel has a better convective heat transfer coefficient compared to conventional porous media. Furthermore, methods to improve the heat and fluid flow inside the aerogel are discussed. This work sheds light on the effective thermal management of various devices where lightness is critical.