Iron oxide nanoparticles have found an increasing number of biomedical applications as sensing or trapping platforms and therapeutic and/or diagnostic agents. Most of these applications are based on their magnetic properties, which may vary depending on the nanoparticle aggregation state and/or concentration. In this work, we assess the effect of the inter- and intra-aggregate magnetic dipolar interactions on the heat dissipation power and AC hysteresis loops upon increasing the nanoparticle concentration and the hydrodynamic aggregate size. We observe different effects produced by inter- (long distance) and intra-aggregate (short distance) interactions, resulting in magnetizing and demagnetizing effects, respectively. Consequently, the heat dissipation power under alternating magnetic fields strongly reflects such different interacting phenomena. The intra-aggregate interaction results were successfully modeled by numerical simulations. A better understanding of magnetic dipolar interactions is mandatory for achieving a reliable magnetic hyperthermia response when nanoparticles are located into biological matrices.