Hiya, I ride my XT660X all year round here in Italy where we get fairly high summer temperatures and I have never felt excessive heat from my engine even in city traffic riding. I have also never heard the fan cut in. So your case sounds very strange.

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(Now sold on, sob) 2011 Blue XT660X with gold wheels, was 26,500 km.
Engine mods: K&N Stage 1 filter, DNA Stage 2 filter, snorkel removed, Kev fuel mod fitted.
Plus: smoked Puig screen, Yam aluminium sump guard, Yamaha / Acerbis handguards, Givi Trekker aluminium side cases, Leo Vince X3 cans plus Kev front fork mod and Fender Xtender. Just fitted Michelin Road Pilot 3 tyres.

SOLD the XTX for a Super Ten 1200. And just bought a Raptor 700 so staying on here for some tips....