Relaxation dynamics of embedded metal nanoparticles after ultrafast laser pulse excitation is driven by thermal phenomena of different origins the accurate description of which is crucial for interpreting experimental results: hot electron gas generation, electron-phonon coupling, heat transfer to the particle environment and heat propagation in the latter. Regardingthis last mechanism, it is well known that heat transport in nanoscale structures and/or at ultrashort timescales may deviate from the predictions of the Fourier law. In these cases heat transport may rather be described by the Boltzmann transport equation. We present a numerical model allowing us to determine the electron and lattice temperature dynamics in a spherical gold nanoparticle core under subpicosecond pulsed excitation, as well as that of the surrounding shell dielectric medium. For this, we have used the electron-phonon coupling equation in the particle with a source term linked with the laser pulse absorption, and the ballistic-diffusive equations for heat conduction in the host medium. Either thermalizing or adiabatic boundary conditions have been considered at the shell external surface. Our results show that the heat transfer rate from the particle to the matrix can be significantly smaller than the prediction of Fourier's law. Consequently, the particle temperature rise is larger and its cooling dynamics might be slower than that obtained by using Fourier's law. This difference is attributed to the nonlocal and nonequilibrium heat conduction in the vicinity of the core nanoparticle. These results are expected to be of great importance for analyzing pump-probe experiments performed on single nanoparticles or nanocomposite media.