Lumped Capacitance Analysis of Coffee?
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You don’t really need to go through the calculations to realize that the heat transfer from the coffee to the cup, and from the cup to the air, is going to be faster if you wait and put the ice in only after the coffee has cooled down to 70ºC. Why? because with either option you’re looking for the same amount of total heat energy to be transported from the coffee to the air. And that heat transfer is going to proceed more quickly for a greater temperature difference between the coffee and the air. So the hotter the coffee, the faster your goal heat-transfer quantity is going to be met.