The difference in temperature and density between a coronal hole and the surrounding corona is primarily driven by the magnetic field configuration. In a standard coronal region, magnetic field lines are complex and closed, trapping hot plasma in loops. However, in a coronal hole, the magnetic field lines are 'open,' meaning they extend far out into the heliosphere rather than looping back to the solar surface.
Because these field lines are open, the plasma is not confined. This allows the particles to escape upward into space, creating a steady outflow known as the solar wind. This continuous expansion causes the plasma to undergo adiabatic cooling, where the rapid increase in volume leads to a significant drop in temperature. Furthermore, as the particles stream away from the Sun, the density decreases because the material is being physically removed from the region through this constant outflow.
In summary, the open magnetic geometry facilitates rapid particle escape and expansion, which simultaneously lowers the plasma density and reduces its temperature through adiabatic processes.