  We propose a computational strategy to quantify the temperature evolution of
the timescales and lengthscales over which dynamic facilitation affects the
relaxation dynamics of glass-forming liquids at low temperatures, that requires
no assumption about the nature of the dynamics. In two glass models, we find
that dynamic facilitation depends strongly on temperature, leading to a
subdiffusive spreading of relaxation events which we characterize using a
temperature-dependent dynamic exponent. We also establish that this temperature
evolution represents a major contribution to the increase of the structural
relaxation time.
