As far as I'm aware, depending on the particular loco class, it's purely down to coolant temperature. So there will be times when the engine is colder than the fan activation temperature, for instance after starting, where the engine is running and the fan isn't turning. Likewise, there will be times where the cooling system has reduced the coolant temperature below the point the fan is switched on when the engine is under light loading.
Under heavy loads the cooling system will struggle to reduce the coolant temperature below the fan activation temperature, so it will run constantly. There are also moving shutters involved as well, obvious on the class 50's, but also present on the 37's AFAIK. The Class 50's have an electrically driven fan, which has two speeds selected automatically depending on coolant temperature, but the refurbished 37's had a mechanical drive controlled by an electro-magnetic clutch linked to the coolant temperature, so probably only one speed.
Reading between the lines, it's possible that the fan rotates continuously on the unrefurbished 37's as it's driven mechanically from the engine.
HTH