X350 3.0 towing / auto box question

[occrj]

Hi all,

Dad's gone and bought a 2003 X350, V6, 3.0 auto.

Although he has no plans to get a tow-bar fitted to it anytime soon (his old 750iL is being kept for caravan duties), he's curious to know whether the X350 would need an auxiliary oil cooler for the auto 'box if he did use it to tow a caravan (heresy I know)??

Thanks, RJ.