That model doesn't explain the relatively sharp drop in the beginning.
Apparently the act of pouring has a huge effect on temperature because of the surface area :: volume ratio of the fluid as it streams (and turbulence after striking the bottom). The site above claims a single pour can drop it 20-30 degrees. There may be a similar effect here.
dT/dt = -k(T_0 - T_room)
so T(t) = T_room + (T_0 - T_room) exp(-kt)
exp(-x) has a fast drop off then levels off.
scroll down, these graphs just don't look similar.
There is another factor here: convection. Its speed depends on the viscosity of the fluid and the temperature difference both. And viscosity itself depends on the temperature, so you get this very sharp dropoff.