In this talk I will present an application of the hyperboloidal formalism to the study of black hole evaporation. I will begin by briefly presenting the formalism for this semiclassical treatment, as well as the causal structures of the spacetimes under study. I will then explain the importance of hyperboloidal foliations which reach past null infinity for the construction of the appropriate quantum state of the field, and present preliminary results of a numerical evolution in this setup.