That's significantly more complicated than one might initially consider.
The outcome will depend on things like air movement and temperature of the ambient environment and what material the cup is made from and heat conductivity of each material involved. In addition, the coffee will be losing some heat as radiant energy, in the form of infrared light and some in the form of thermal energy. Does every material give off the same mixture of each? -- that's also a question your model is going to have an answer for. Also, some of the heat bounces back depending on what surface the cup is on and what the air mixture is by molecule.
You could just plug-in some algorithms of your own to mirror your observations as closely as possible, which is what is usually done in the videogame programming world, but then it really sort of matters how accurate you want your model. Ray tracing is such a big deal in today's computer world because it's a way to accurately capture the behavior of light that our hardware can almost touch in realtime. Of course, it becomes easier the more rules your code ignores and everything screeches to a halt when we try to mirror it exactly (infinite reflection).
In any case, I'm just ranting. What was your question again?