  We perform 2D, fully compressible, time-implicit simulations of convection in
a solar-like model with the MUSIC code. Our main motivation is to explore the
impact of a common tactic adopted in numerical simulations of convection that
use realistic stellar conditions. This tactic is to artificially increase the
luminosity and to modify the thermal diffusivity of the reference stellar
model. This work focuses on the impact of these modifications on convective
penetration (or overshooting) at the base of the convective envelope of a
solar-like model. We explore a range of enhancement factors for the energy
input and confirm the increase in the characteristic overshooting depth with
the increase in the energy input. Our results highlight the importance of the
impact of penetrative downflows on the thermal background below the convective
boundary. This is a result of compression and shear which induce local heating
and thermal mixing. The artificial increase in the energy flux intensifies the
heating process by increasing the velocities in the convective zone and at the
convective boundary, revealing a subtle connection between the local heating of
the thermal background and the plume dynamics. This heating also increases the
efficiency of heat transport by radiation which may counterbalance further
heating and helps to establish a steady state. The modification of the thermal
background by penetrative plumes impacts the width of the overshooting layer.
Our results suggest that an artificial modification of the radiative
diffusivity in the overshooting layer, rather than only accelerating the
thermal relaxation, could also alter the dynamics of the penetrating plumes and
thus the width of the overshooting layer. Results from simulations with an
artificial modification of the energy flux and of the thermal diffusivity
should be regarded with caution if used to determine an overshooting width.
