The propagation of intense rectangular thermal pulses in superfluid helium is studied numerically using superfluid turbulence hydrodynamics with various equations for vortex line density dynamics. It is shown that the experimental data are most adequately described by the Vinen equation. The impact of the background vortex line density on the dynamics of the pulses at different temperatures of the unperturbed fluid is studied by using the Vinen equation that describes the vortex line density dynamics. It is found that a high background vortex line density leads to a significant change in the pulse shape and overheating of the fluid. At the same values of the heat flux supplied to the heater and the background vortex line density, the temperature perturbations decrease with the increasing temperature of the unperturbed fluid. This is due to changes in the thermodynamic properties of the fluid and the vortex line density dynamics. As the temperature increases, the increase in the vortex line density slows down, as a result of which the fluid temperature perturbations decrease significantly.