In this thesis, we numerically investigate the thermal dynamics and stability of two types of core/shell coherent plasmonic nanoscale light sources (spasers): the first structure has an oblate geometry and consists of a gain core encapsulated by a metal shell, while the second structure has a prolate metal core surrounded by a gain shell. We identify three main contributions to heating in spasers: the decay of resonant surface plasmons due to Ohmic loss at the spasing frequency (520 nm, heats metal), the thermalization of single-electron excitations (and to a lesser degree, also the decay of surface plasmons) at the pumping frequency (470 nm, heats metal) and the decay of electronic states into vibronic excitations of the chromophores (heats gain material). We simulate full-wave optics of nonlinear media, using Maxwellís equations coupled to the heat equation, to accurately predict the transient thermal behavior of an operating spaser. The term "nonlinear media" refers to gain media with nonlinear saturation that depends on local field intensity. The coupling of the differential equations is done with a temperature-dependent metal dielectric function, whose changes are described with a model based on Drude-fitting with variable collision frequency. We describe the selection process for spaser geometries with respect to their experimental realizability, and establish criteria for the comparison of the operation of different spasers. We further give theoretical arguments explaining why the continuous-wave operation might be difficult to achieve for some spasers. However, we demonstrate that the considered spasers can reliably operate in pulsed regime with durations up to 110 ps and 45 ps, respectively, which are reasonably long pulse lengths.