  Recent hydrodynamical simulations of convection in a solar-like model suggest
that penetrative convective flows at the boundary of the convective envelope
modify the thermal background in the overshooting layer. Based on these
results, we implement in one-dimensional stellar evolution codes a simple
prescription to modify the temperature gradient below the convective boundary
of a solar model. This simple prescription qualitatively reproduces the
behaviour found in the hydrodynamical simulations, namely a local heating and
smoothing of the temperature gradient below the convective boundary. We show
that introducing local heating in the overshooting layer can reduce the
sound-speed discrepancy usually reported between solar models and the structure
of the Sun inferred from helioseismology. It also affects key quantities in the
convective envelope, such as the density, the entropy, and the speed of sound.
These effects could help reduce the discrepancies between solar models and
observed constraints based on seismic inversions of the Ledoux discriminant.
Since mixing due to overshooting and local heating are the result of the same
convective penetration process, the goal of this work is to invite solar
modellers to consider both processes for a more consistent approach.
