On a digi injection car the fuel pressure is always the same, this is maintained by the FPR and temperature does not effect it.
On a k-jet car again the fuel pressure inside the main body of the metering head is always the same, around 5 bar. This is maintained by a pressure relief valve inside the metering head, and is not effected by temperature.
For cold running the WUR actually reduces the fuel pressure to the chamber above the fuel metering pin, allowing it to travel higher for any given air meter flap movement, increasing the fuel volume. This pressure is gradually increased as the car warms up.
Also the WUR mod reduces the fuel pressure to the pin (warm control pressure), from the factory value of 49-55PSI, to around 48PSI, allowing the pin to move higher, increasing the volume delivered.