The design of lightweight and stiff structures with attractive vibration damping properties is a major issue in mechanical engineering. The insertion of Acoustic Black Holes in a beam (1D ABH) is an innovative technique that consists in locally reducing the thickness at the beam end and coating it with a viscoelastic film. The reflection coefficient R of the resulting beam termination decreases with frequency and displays typical arches for which each drop corresponds to the resonance of a trapped mode localized in the ABH profile. In particular, it can be shown that a drop of R can perfectly vanish when the amount of losses is well adjusted so that critical coupling conditions are achieved. However, the precise amount of added damping for fulfilling the critical coupling conditions is particularly difficult to tune by using only classical visco-elastic layers. It is here proposed to control it by using a thermal active system acting in a shape memory polymer (SMP). The goal of the paper is to investigate experimentally several enhanced ABH (eABH) for which the damping and the stiffness profiles are controlled using a thermal active system. The eABH of this study consists in an architectured SMP layer controlled in temperature along the ABH pit of power law profile. For each eABH configuration, the trajectory of the zeros of R induced by a change in the thermal profile is studied in order to adjust the amount of losses and approach the critical coupling conditions.