The optical and thermoplasmonic properties of bimetallic nanoparticles (NPs) offer a wide range of possibilities for designing functional materials and innovative nanotechnological devices. Their exploration is generating increasing interest in experimental and theoretical scientific research. The combination of noble metals such as gold (Au) and silver (Ag) within the same nanostructure, in the form of an alloy or core/shell arrangement, presents several advantages and potential applications. In this paper, the finite element method (FEM) is used to study the optical response and nanoscale heat generation capability of bimetallic core/shell nanospheres composed of a mixed alloy (AuxAg1−x)-core and an Au-shell. First, we studied the surface plasmon resonance (SPR) properties by generating absorption spectra. Our results show that the position and amplitude of the SPR peak of these nanospheres are strongly influenced by the fractions of Au and Ag metals composing the core, as well as by the Au-shell thickness. In particular, the SPR-peak position can be adjusted between 535nm and 1085nm depending on the composition and structure of these NPs. Secondly, we studied the ability of these NPs to convert absorbed light into heat when exposed to either a continuous wave (cw) laser or a femtosecond pulsed (fs-pulsed) laser. The results demonstrate the ability to control the temperature generated by these NPs based on the core composition, Au-shell thickness, illumination intensity, and the type of illumination (cw or fs-pulsed). In particular, under fs-pulsed illumination, the internal temperature of the NPs is significantly higher than under cw illumination. These findings are crucial for the use of these alloy-core and Au-shell nanoparticles in various thermoplasmonic applications.