If it's for a game, it's got to be a pretty strange game where the incompressible assumption causes problems.

If it's for an engineering problem, there are off the shelf products both paid and open to solve fluid problems. Computational Fluid Dynamics code.

If it's purely to learn and play:

When you lose the incompressible assumption it becomes simultaneously a fluid dynamics and thermodynamics problem.

You will need to learn about:

The basic laws of thermodynamics

It's a big subject and it's hard to advise you more specifically without knowing where you are starting from.