Other people have answered, but I think this is slightly more intuitive way to put it:
Newton's law of cooling states that the rate of temperature reduction (heat loss) of a body is proportional to the temperature delta between it and its ambient surroundings. We can write this as:
dT/dt = kT
Where T is temperature delta, t is time, and k is some proportionality constant. So the rate of cooling is changing as the delta temperature reduces, specifically, it is getting exponentially reducing as it gets closer to thermodynamic equilibrium (where no heat is exchanged):
T(t) = Ce^kt
C = T(0)
Which means there is a larger cool down with the hot water at first, but under this simple model, once the T(t) hits the same temperature of the cool water it's being compared to, it's cooling rate should be equivalent (and a lot slower).
dT/dt = kT
Where T is temperature delta, t is time, and k is some proportionality constant. So the rate of cooling is changing as the delta temperature reduces, specifically, it is getting exponentially reducing as it gets closer to thermodynamic equilibrium (where no heat is exchanged):
T(t) = Ce^kt C = T(0)
Which means there is a larger cool down with the hot water at first, but under this simple model, once the T(t) hits the same temperature of the cool water it's being compared to, it's cooling rate should be equivalent (and a lot slower).