How do you know he was a bastard? Were you there when his wife got captured by Tatars (was it ._. not sure i forgot their name), though it is highly likely that he might of not been Genghis' son, how the fuck do you know?
Thousands of Mongols and Turks, particularly in the North, were Temujin Hagan was born, exhibit red and blonde hair and blue eyes, as a result of centuries of interbreeding with Slavs and Germanics in Russia and the Baltic states.
Mongols and other Central Asian peoples sometimes have fairer skin with red hair, I believe. Some sources say that Genghis Khan and many of his sons had red hair, but I don't think any of those sources are firsthand accounts, so we don't know for sure.