After the fuel goes through the fuel filter element, it goes to the hydromechanical unit (HMU) (RR = FMU). The HMU meters the fuel. The fuel goes from the HMU to the fuel flow transmitter and then back to the HMU. The HMU distributes the fuel into the fuel supply manifolds. The fuel supply manifolds send the fuel to the fuel nozzles.
The fuel feed on the RR is slightly different...
tank pumps ~ LP side of engine pump~fuel-cooled oil cooler ~ LP Fuel Filter ~ HP side of engine pump ~ Fuel Metering Unit (with fuel return to HP engine pump) ~ FF Transmitter ~ HP Fuel Filter ~ Fuel Manifold/Spray Nozzles.
Is there only one (common) fuel temperature sensor for the fuel to both engines?
I don't think you could call it "common"... The crew only know the temperature of the fuel in the left tank. Only God knows what the temperature is in the right and centre tanks
On the 747-400, it is only known what the fuel temperature is in one of (up to) 9 tanks. Boeing, I'm sure did their tests and found that the left tank is always coldest. Whether this is true for an aircraft flying east to west (with the left wing in sunshine and the right wing in the shadow of the fuselage), I can't say... I don't know if this is negligible or not (compared to, say, ram air rise).