Aggregates of magnetic nanoparticles (MNPs) exhibit unusual properties due to the interplay of small system size and long-range dipole-dipole interactions. Using the micromagnetic simulation software OOMMF, we study the spin morphologies and heat dissipation in micron-size spherical assemblies of MNPs. In particular, we examine the sensitivity of these properties to the dipolar strength, manipulated by the interparticle separation. As OOMMF is not designed for such a study, we have incorporated a novel scaling protocol for this purpose. We believe that it is essential for all studies where volume fractions are varied. Our main results are as follows: (i) Dense assemblies exhibit strong dipolar effects which yield local magnetic order in the core but not on the surface, where moments are randomly oriented. (ii) The probability distribution of ground-state energy exhibits a long high-energy tail for surface spins in contrast to small tails for the core spins. Consequently, there is a wide variation in the energy of surface spins but not the core spins. (iii) There is strong correlation between ground-state energy and heating properties on application of an oscillating magnetic field h(t) = h o cos 2πf t: the particles in the core heat uniformly, while those on the surface exhibit a wide range from cold to intensely hot. (iv) Specific choices of h o and f yield characteristic spatial heat distributions, e.g., hot surface and cold core, or vice versa. (iv) For all values of h o and f that we consider, heating was maximum at a specific volume fraction. These results are especially relevant in the context of contemporary applications such as hyperthermia and chemotherapy, and also for novel materials such as smart polymer beads and superspin glasses.