For clinical hyperthermia treatment the heating efficiency of magnetic nanoparticle ensembles is a crucial element. Using efficient algorithms, this heating is studied numerically with a focus on the effects of dipole-dipole interparticle interactions. For the time evolution of realistically modeled systems an approach based on the Landau-Lifschitz-Gilbert equation of motion with Langevin dynamics is taken. Our results suggest a widely negative influence of dipole-dipole interactions on the heating power of nanoparticles. However, considering ensembles within a fixed, given sample volume an optimal particle density exists. The presented results may have important implications for the medical use of magnetic hyperthermia treatment.