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.
Ha. My university professor used this in a lab to catch people who slack 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.
https://www.electronics-tutorials.ws/rc/time-constant.html
scroll down, these graphs just don't look similar.