Accretion disks are observed around young stellar objects such as T Tauri stars. In order to complete the star formation, particles in the disk need to loose angular momentum in order to be accreted into the central object. The magneto-rotational instability (MRI) is probably the mechanism responsible for a magneto-hydrodynamic (MHD) turbulence that leads to disk accretion, which implies the disk particles to be coupled with the magnetic filed lines. As the temperature in the disk is low, we considered, besides the viscous heating mechanism often included in the models by means of the α - prescription, the damping of Alfvén waves as an additional heating source. In particular, we show that the mechanism derived that couples the turbulent and non-linear damping mechanisms of Alfvén waves proved to be very efficient, generating temperatures almost one order of magnitude higher than those mechanisms considered independently.