Afaik the bypass on the oil side is thermostatic, and diverts oil flow through or around the FOHE to maintain oil temperature. It is designed to cope with a wide range of fuel temperatures from freshly loaded ambient to altitude-soaked cold. With very cold fuel, most oil will bypass the cooler with only a bare minimum passing through to maintain oil temperature. The heating effect on the fuel will be minimal.
Sooty
Sorry sooty but the AMM doesn't agree with you
AMM 79-20
* Oil pressure relief bypass valve
If the engine oil is too cold or the heat exchanger oil core is
clogged, the pressure relief bypass valve opens.
The fuel temp does not affect the operation at all. Only oil temp. And by too cold RR mean around zero deg C.