Ah, the model you articulate here suggests that the convective currents prevalent in an (initially) hotter pot of water as it cools, is what drives the higher r

Ah, the model you articulate here suggests that the convective currents prevalent in an (initially) hotter pot of water as it cools, is what drives the higher rate of heat energy loss as compared with a pot of water initially at a uniform temperature matching ambient. As convection does indeed exchange heat faster than conduction, then so long as the differential temperature between top and bottom continues as the pot cools, (and yes the fluid flow does trivially have fluid momentum i.e. inertia mentioned above), then there is a case that it can continhe to lose heat energy faster than the relatively still flowing, initially room temperature, pot of water.