Newton's Law of Cooling

When a hot object is left in a cooler room — or a cold drink is left on a warm table — its temperature doesn't change at a constant rate; it changes fastest when the gap between the object and its surroundings is largest, and slows as the two temperatures converge. Newton's Law of Cooling captures this precisely: the rate of change of a body's temperature $T$ is proportional to the difference between $T$ and the temperature $A$ of the surrounding medium.

where $k > 0$ is a constant. The sign of $T - A$ tells you the direction of change: if $T > A$, the temperature is decreasing over time and the body is cooling; if $T < A$, the temperature is increasing over time and the body is heating — in both cases, $T$ moves toward $A$, never away from it. …