The rolled up newspaper test used to be the first test of any BMW cooling system a few years ago. This really just tested how bunched the fan's viscous coupling was. If the fan stopped rotating when a lightly applied rolled up newspaper was touched off the edge of the fan blades then it needed replacing.

As these cars are a bit older now there seems to be a whole load of new, mostly age related, issues to look at and others here probably have more relevant experience than me.

Having said that, its still a good place to start.