Are you sure? I believe Newtown's law of cooling says the temperature will drop sharply at the beginning:
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.
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.
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.
scroll down, these graphs just don't look similar.