The use of magnetic nanoparticles (MNPs) to locally increase the temperature at the nanoscale under the remote application of alternating magnetic fields (magnetic particle hyperthermia, MHT) has become an important subject of nanomedicine multidisciplinary research, focusing among other topics on the optimization of the heating performance of MNPs and their assemblies under the effect of the magnetic field. We report experimental data of heat released by MNPs using a wide range of anisometric shapes and their assemblies in different media. We outline a basic theoretical investigation, which assists the interpretation of the experimental data, including the effect of the size, shape and assembly of MNPs on the MNPs' hysteresis loops and the maximum heat delivered. We report heat release data of anisometric MNPs, including nanodisks, spindles (elongated nanoparticles) and nanocubes, analysing, for a given shape, the size dependence. We study the MNPs either acting as individuals or assembled through a magnetic-field-assisted method. Thus, the physical geometrical arrangement of these anisometric particles, the magnetization switching and the heat release (by means of the determination of the specific adsorption rate, SAR values) under the application of AC fields have been analysed and compared in aqueous suspensions and after immobilization in agar matrix mimicking the tumour environment. The different nano-systems were analysed when dispersed at random or in assembled configurations. We report a systematic fall in the SAR for all anisometric MNPs randomly embedded in a viscous environment. However, certain anisometric shapes will have a less marked, an almost total preservation or even an increase in SAR when embedded in a viscous environment with certain orientation, in contrast to the measurements in water solution. Discrepancies between theoretical and experimental values reflect the complexity of the systems due to the interplay of different factors such as size, shape and nanoparticle assembly due to magnetic interactions. We demonstrate that magnetic assembly holds great potential for producing materials with high functional and structural diversity, as we transform our nanoscale building blocks (anisometric MNPs) into a material displaying enhanced SAR properties.