Rover owners: Steppie CVT gearbox cooling

Whilst at a track day yesterday and as a result of engine temperature problems on the way home, I got to thinking about gearbox cooling and I'm now thinking of adding a cooling fan to the oil cooler for the CVT gearbox.

The rationale for this is as follows:

After each track session the engine got pretty hot and to cool it down while back in the paddock I left the engine running a short while so any residual engine heat was taken from the engine by the engine coolant radiator and its fan.

Whilst the CVT gearbox has a cooler it has no forced air fan so no cooling can be achieved when stationary and as we all know the CVT gearboxes are delicate little flowers and need their special oil and persumably like it cooled too! The CVT oil both lubricates and cools the clutches, pulleys and belts within.

The CVT gear box oil cooler sits in front of the engine coolant radiator and whilst this will cool the gearbox oil when moving it won't do much whilst stationary.

Therefore I think that an electric fan is needed to force air through the gearbox oil cooler. When the engine is running the oil pump in the gearbox runs so circulating oil around the cooler. I'm thinking forced cooling of the oil would be a good idea. I'm looking at getting a 120mm waterproof 12v fan or similar and fixing it in front of the oil cooler.

Any comments...other than don't track day your Steppie?