It is not as important as it may seem. While the shell will get
quite hot, not much of that heat gets beyond the shell. When the unit
is operating it is drawing lots of air in and that air is at air
temperature and it is that temperature that the system really sees.
While there is some heat being radiated from the shell, it is only a
minor component. The real factor is the air temperature.

It is possible to spray water on the unit and increase efficiency
and in your area that should be efferent, but, it can also result in
build up of deposits unless you are flooding the coils.

Adding an additional sun shade would be just adding an additional
shell.