I am slightly familiar with cold soaked fuel, however never considered it in this instance as the aircraft had been flying short sectors and on the previous sector the departure point was at +12.
Totally irrelevant what the departure point temperature was. Temperature reduction with altitude is approximately 2C/1000’. So, at 6,000’ cruise on your “short sector” (unlikely cruise altitude, by the way), the OAT would be 0C and very likely to be in the moderate/severe icing range if flying in cloud.