In this work, we conduct a comprehensive computational study of the optical and photothermal properties of multifunctional α-Fe2O3/Au/SiO2 nanorice matryoshka nanoparticles using a combination of boundary element method, finite element method, and discontinuous Galerkin time-domain method. The magnetic core in the nanorice allows their use as a contrast agent in nuclear magnetic resonance technique as well as dragging and rotating the nanoparticles with an external magnetic field, while the plasmonic counterpart enables the excitation of localized surface plasmon resonances. We show that both longitudinal and transverse plasmonic resonances induced within the hybrid asymmetric nanoparticle can be sintonized into the 650–900 nm range of the electromagnetic spectrum, where the absorption of tissue is minimal. Thus, it is possible to heat the nanoparticle’s local surrounding environment, making the proposed nanorice particles good candidates for thermal ablation treatment of cancer cells. We show that the local temperature in the nanorice surroundings can be increased by up to 80 K while illuminating the hybrid system at the resonant frequency of the longitudinal plasmon mode with typical and reasonable optical power density of 5 W/cm2.