wanabee, it took quite some time before the values started getting real low.
In the beginning the "warm" fuel quantity is big but as the flight progresses, reducing fuel quantities receive the same cold "energy" and thus temps are falling quicker.
Long flights into very long winter nights in the northern hemisphere gets the plane eventually cold soaked.
If I remember correctly problems started after 5-7 hours into a typical flight from AMS-NRT or the likes.