[ephbit]

These temperature gradients obviously lead to convection.

Stronger convection means greater heat transfer, thus greater rate of cooling down.

But it'd be surprising if the inertia of the convection of the initially hot system didn't just gradually decline (because of friction) to almost exactly (little bit greater) the same level of convection (which the initially cool system had in the beginning) when it reaches the same average temperature.

[londons_explore]

Water currents can last a surprisingly long time. Pour one liquid into another of a slightly different color and the swirling mixing process can go on for minutes at least. Perhaps hours in the right circumstances.