There is a strong interest in the use of plasmonic metal nanoparticles in medical applications involving photothermal therapy. In this study, the problem of calculating the temperature elevation of a fluid arising from the absorption of light by a suspension of plasmonic nanoparticles is examined. The dependence of this temperature increase on the absorption cross section of nanoparticles of different shapes, in particular, nanospheres, nanospheroids, and nanostars, is studied. The nanoparticles behave as point sources of heat production and the time-dependent heat transfer equation is solved assuming that the nanoparticles are confined to a limited region. From this solution, the steady-state temperature of the fluid medium can be calculated and the time constant to achieve this temperature determined.