I have the run on switch for the Urban cooling fan and it does help cool the heads after a run. As in my +8 the run on of the fan after turning off the engine helps cool things down, rather than the dead stop. Has no ill effects on the battery.
Bruce 1964 4/4 Series V Comp (Megan) 1994 +8 (Maurice) 2013 M3W (Olga)