Under illumination at their plasmonic resonance wavelength, metal nanoparticles can turn into efficient nanosources of heat by light absorption. Heating a small volume makes it possible to achieve fast dynamics. In this article, we investigate theoretically, numerically and experimentally the temperature distribution of a plasmonic system generated by a modulated incoming light. In particular, we study the response in amplitude and phase of the temperature variations. The cases of single and multiple nanoparticles are both addressed. Many parameters are discussed such as the nature of the media (nanoparticle and surroundings), the size of the nanoparticle or of the plasmonic system, the nanoparticle interdistance, the frequency of the modulation, a possible finite surface thermal conductivity of the nanoparticles and the dimensionality of the system. This work is also intended to determine how fast a plasmonic system is able to induce temperature variations in its surrounding medium.