I was thinking of a 12-ounce styrofoam cup. That's what we have at work... might even make the calculations easier. I like the idea of making this an online problem. I'll even volunteer to get real life data with some thermocouples and real cups of coffee!

In the case of axi-symmetric styrofoam coffee cup, the heat loss would come mainly from the evaporation at the liquid surface because the styrofoam is a very good insulating material. The natural convection inside the coffee probably is not very important other than that it circulates the cofee and make the temperature in the coffee more uniform.( it would be important if you use an electric fan over the coffee to lower the surface temperature rapidly). The Qdot due to the evaporation is related to the coffee temperature, ambient temperature, pressure, humidity, and nature convection above the coffee cup. The temperature difference would definitely affect the nature convection above the cup and thus the rate of evaporation. So if we can somehow estimate the rate of evaporation ( loss of coffee) then we can compute the heat loss due to evaporation ( energy required to turn the coffee into vapor ). In a way, it is similar to the evaporative cooler ( use the water to cool the air by evaporation). So the key issue in this case is : how to model the evaporation and nature convection above the cup.

One cheap and quick experiment is worth a thousand CFD simulations. Off to make two cups of coffees now ...

This brings to mind the frothy cup of cappucino or a bubble bath that stays warm longer on a cold day then the average cup of coffee or clear tub of hot water ...

It is always a good idea to validate the result by testing. By the way, if you let the coffee to sit overnight, it will probably reach the room temperature. Then, you spend 5 seconds to add the cold milk to the coffee. The coffee temperature at this point will be colder than the room temperature. On the other hand, if you add the cold milk to the hot coffee in 5 seconds and let it sit overnight. The coffee temperature at that time will reach the room temperature. The coffee temperature will be different at the end of ( 5 seconds plus overnight ). The key issue in this case is : the heat is constantly being removed from the milk as long as it remains inside the refrigerator. In other words, if you let the milk sit outside the refrigerator overnight, then it will also reach the room temperature. In this case, the coffee temperature will be the same .