Graphene is an ideal material for integrated nonlinear optics thanks to its strong light-matter interaction and large nonlinear optical susceptibility. Graphene has been used in optical modulators, saturable absorbers, nonlinear frequency converters, and broadband light emitters. For the latter application, a key requirement is the ability to control and engineer the emission wavelength and bandwidth, as well as the electronic temperature of graphene. Here, we demonstrate that the emission wavelength of graphene$\prime$ s broadband hot carrier photoluminescence can be tuned by integration on photonic cavities, while thermal management can be achieved by out-of-plane heat transfer to hexagonal boron nitride. Our results pave the way to graphene-based ultrafast broadband light emitters with tunable emission.