  How a closed system thermalizes, especially in the absence of global
conservation laws but in the presence of disorder and interactions, is one of
the central questions in non-equilibrium statistical mechanics. We explore this
for a disordered, periodically driven Ising chain. Our numerical results reveal
inhomogeneous thermalization leading to a distribution of thermalization
timescales within a single disordered sample, which we encode via a
distribution of effective local temperatures. Using this, we find an excellent
collapse $\textit{without}$ $\textit{any}$ $\textit{fitting}$
$\textit{parameters}$ of the local relaxation dynamics for the entire range of
disorder values in the ergodic regime when adapting the disorder-averaged
diagonal entanglement entropy as internal `time' of the system. This approach
evidences a remarkably uniform parametrization of the dynamical many-body
evolution of local temperature within the otherwise highly heterogeneous
ergodic regime, independent of the strength of the disorder.
