It is a classic physics question… “If you require the tea to stay warmer for longer, should you put the milk in straight away or wait until you want to drink it?”
People give random explanations ranging from common sense to differential equation examples centred about temperature gradients. I thought the best thing to do was test it. Together with the misses (yes she supports me in my random whims) we made 4 identical sups of tea (same water, time cups etc) and put a thermometer in each. An identical amount of milk (all chilled to the same temperature) was added at different times. Milk was added to the first mug as soon as we started the experiment, 3 minutes later for the next mug, then at 6 minutes for the next mug, then at 9 minutes for the last mug. Temperature readings were taken at 30 second intervals throughout. The results are shown in the graph below.
We can see from the graph that there is no long-term difference. There is a sudden drop in temperature as the milk is added, as expected, but all the lines converge quickly.