In photothermal cancer therapy, gold nanoparticles and silica-gold nanoshells of specific shapes are used in order to generate heat by excitation of plasmons. We have investigated a different mechanism for heating metal nanoparticles: the Joule effect, whereby the energy resonantly absorbed from laser radiation first dissipates in electron processes before being finally converted into lattice vibrations. For this mechanism to exist, the electronic structure of the nanoparticulate material must possess enhanced densities of states at the Fermi energy and within the energy range 1.3 to 1.9 eV above it, i.e., in the transparency window of the biological tissues. Numerical estimations indicate that Fe-, Mo-, and Ta-doped gold, and Fe-doped tantalum are plausible materials for non-plasmonic hyperthermia. No special conditions concerning the shapes or inner structure of nanoparticles are imposed, which is an advantage over existing techniques.