Pressure (black), temperature (red) and density (blue) profiles as a function of depth (expressed by the Lagrangian coordinate, i.e. the mass m), for the reference adiabatic (solid curves) and semiconvective (dashed curves) cases of Saturn a) and Jupiter b). The increased thermal gradient due to the inefficient heat transport in the semiconvective case (with N_l = 10^4.5 for Jupiter and 10^5.4 for Saturn) strongly increases the internal temperature. This causes a partial redistribution of the core material within the gaseous envelope.