I'm afraid "fine when cold" is a common faulty pump symptom.
When its cold the fluid viscosity is higher so its easier for the pump to generate higher pressure. Once the engine and pump have been operating even briefly, the oil viscosity reduces & eg if there are internal leaks within the pump, the pump output will drop.
The pump is designed to generate the required 100+ bar pressure for full assistance at engine idle & then a pressure limiting valve keeps it at that pressure as the engine speed increases so the assistance doesn't vary at different engine speeds.
If revving the engine gives you more assistance, it means the pump isn't generating the designed pressure at idle, but increases output at higher rotation speed,
Those are exactly the same symptoms I had on our RR.
I tested & changed the servotronic valve & the Body Control unit, but found no faults / change in symptoms before finally accepting I'd have to break into & test the hydraulics. I even connected the servotronic valve to a permanent 12v supply to eliminate electrical control issues & maximise the servotronic additional assistance. Steering was still really heavy at idle/ vehicle stationary.
I fitted a pressure gauge to check the pump output & I was only getting 10 bar at idle and 30 bar at 3000 rpm (It should develop 110 bar at idle and above).
I fitted a replacement second hand pump & problem was gone - 110bar from engine idle upwards.
