Nanostructured magnetic systems have many applications, including potential use in cancer therapy deriving from their ability to heat in alternating magnetic fields. In this work we explore the influence of particle chain formation on the normalized heating properties, or specific loss power (SLP) of both low- (spherical) and high- (parallelepiped) anisotropy ferrite-based magnetic fluids. Analysis of ferromagnetic resonance (FMR) data shows that high particle concentrations correlate with increasing chain length producing decreasing SLP. Monte Carlo simulations corroborate the FMR results. We propose a theoretical model describing dipole interactions valid for the linear response regime to explain the observed trends. This model predicts optimum particle sizes for hyperthermia to about 30% smaller than those previously predicted, depending on the nanoparticle parameters and chain size. Also, optimum chain lengths depended on nanoparticle surface-to-surface distance. Our results might have important implications to cancer treatment and could motivate new strategies to optimize magnetic hyperthermia.