Space-borne missions CoRoT and {it Kepler} are providing a rich harvest of high-quality constraints on solar-like pulsators. Among the seismic parameters, mode damping rates remains poorly understood and thus barely used to infer physical properties of stars. Nevertheless, thanks to CoRoT and {it Kepler} space-crafts it is now possible to measure damping rates for hundreds of main-sequence and thousands of red-giant stars with an unprecedented precision. By using a non-adiabatic pulsation code including a time-dependent convection treatment, we compute damping rates for stellar models representative for solar-like pulsators from the main-sequence to the red-giant phase. This allows us to reproduce the observations of both CoRoT and {it Kepler}, which validates our modeling of mode damping rates and thus the underlying physical mechanisms included in the modeling. Actually, by considering the perturbations of turbulent pressure and entropy (including perturbation of the dissipation rate of turbulent energy into heat) by the oscillation in our computation, we succeed in reproducing the observed relation between damping rates and effective temperature. Moreover, we discuss the physical reasons for mode damping rates to scale with effective temperature, as observationally exhibited. Finally, this opens the way for the use of mode damping rates to probe turbulent convection in solar-like stars.