We performed two-dimensional, 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 (or stellar luminosity) and confirm the increase in the characteristic overshooting depth with the increase in the energy input, as suggested by analytical models and by previous numerical simulations. We performed high-order moments analysis of the temperature fluctuations for moderate enhancement factors and find similar flow structure in the convective envelope and the penetration region, independently of the enhancement factor. As a major finding, 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. We suggest that the modification of the thermal background by penetrative plumes impacts the width of the overshooting layer. Additionally, 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 thus be regarded with caution if used to determine an overshooting distance.