Radiofrequency heating of gold nanoparticles for cancer treatment has seen intensive interest during the last decade, but the debate on understanding the physical heating mechanisms is still ongoing. While the electrophoretic oscillation of charged nanoparticles is increasingly being favoured, a recent report is rousing the discussion of Joule heating in prolate shaped nanoparticles. In this paper, we continue this route with the extension for the case of coated ellipsoidal nanoparticles as a means of modelling the effect organic ligands has on the electromagnetic absorption of biological tissue. We observe that introducing a dielectric coating to the metallic nanoparticle increases the absorption for particle aspect ratios that would otherwise be low or moderate, thus improving the flexibility of particle sizes that can potentially be used in treatment.