Nanophotonics is an important branch of modern optics dealing with light–matter interaction at the nanoscale. Nanoparticles can exhibit enhanced light absorption under illumination by light, and they become nanoscale sources of heat that can be precisely controlled and manipulated. For metal nanoparticles, such effects have been studied in the framework of thermoplasmonics, which, similar to plasmonics itself, has a number of limitations. Recently emerged all-dielectric resonant nanophotonics is associated with optically induced electric and magnetic Mie resonances, and this field hasdeveloped very rapidly over the past decade. As a result, thermoplasmonics is being complemented by all-dielectric thermonanophotonics with many important applications such as photothermal cancer therapy, drug and gene delivery, nanochemistry, and photothermal imaging. This review paper aims to introduce this new field of non-plasmonic nanophotonics and discuss associated thermally induced processes at the nanoscale.