Not really. You just need good data or approximations of the data. Then just compute.
We literally don't know what gases, and how much of them, will evaporate off of it until they do evaporate. And that doesn't happen until it warms up more.
Let me just code that up real fast.
In much simpler form, it's similar to the "Where will this satellite in a decaying orbit land?"
The difficulty is not the approximation: the difficulty is that whether drag begins to increase at t=x or t=x+30sec (based on orientation when it first encounters atmosphere) cascades throughout the rest of the equations and dramatically changes the results.