I can only take a guess here. The white may be a thermistor. Since it is in series, I can't imagine it being a fuse. A thermistor, has a given resistance for a given temp. As the temp goes up, the resistance goes down. This would keep the fan at a slightly lower speed, when first turned on, but if heat built up, would slowly increase the fan speed.
I don't know this for sure, just a guess, and about the only thing that makes sense to me anyway.
2012 Ford F250 ext. Cab 4x4
2002 Jeep Wrangler Sahara
2008 Yamaha V-Star 650 Classic
2008 Work and Play 18LT