Milk now, or milk later?

This is a classic physics-class example of Newton's law of cooling: an object's cooling rate is proportional to its temperature difference from the surroundings, so a hotter cup of coffee loses heat faster than a lukewarm one. Adding cold milk right away drops the temperature immediately, which shrinks that difference and slows the rest of the cooling — so despite spending the whole wait cooler, the milk-now coffee ends up warmer than coffee that stayed hot (and cooled faster) only to get the same milk dumped in cold at the end. The gap is small but always in milk-now's favour, for any wait time or cooling rate above zero. Simplifications made here: milk and coffee are both treated as water for heat-capacity purposes (real dairy fat/solids shift this slightly), the mug's own heat capacity and any evaporative cooling from the coffee's surface are ignored, and k is held constant over time though in reality it depends on the mug material, whether it's lidded, and airflow in the room — 0.03–0.12 per minute is a realistic range for an open mug cooling toward room temperature over tens of minutes.