These features are nicely captured by Dynamical Mean-Field Theory (DMFT).
An interesting question is whether this low-temperature scale can be captured in simpler theories.
The phase diagram at half filling is shown below. Note how near the Mott insulator T_coh is orders of magnitude smaller than W/2, the scale of the Fermi temperature for U=0. It is also much smaller than this scale multiplied by Z, the band renormalisation due to interactions.