Lu, while your scenario when the fire goes out is reasonable, it seems that the first ECAM indications of Low Oil Temp and High Oil Pressure appeared when the engines were still running.
Now while the fuel temperature will be somewhere between ambient temperature at altitude and temperature at takeoff, the cooling effect from a dense fluid of higher temperature can be higher than that of a less dense fluid at lower temperature -- and the density of fuel is some thousands of times that of air.
And we haven't even worked in the heat of evaporation
