Berendsen

I am trying to apply Berendsen thermostat for CNT. When I choose to leave one third of the tube atoms to evolve freely with out distrubing the momentum, I am unable to acheive the target temperature and further temperature increases gradually over the whole simulation run (even with a thermostat parameter equals to the timestep i.e., like a simple scaling). How it is possible to acheive target temperature,by scaling only a part of atoms, using some scaling value which should actually scales all the atoms momenta.