My 2004 VP RPMs go up and down approx 500 RPMs slowly flattening out until it warms up. This is going on 5 yrs. Why? Is it an easy fix? thanks

 

Is this occurring in drive, light throttle and going between 35 and 45mph?

 

I think all the early cars do this, certainly mine, a 2003, did it. There seems to be no cure apart from replacing the torque converter, but nobody can tell you why. I just used to put the car in 5 or 4, and wait for a few miles before reverting to D. AFAIK it doesn't do any damage, and on mine I started at 30k and part-exed the car in late 2016 for a 2007 X358 Sovereign when it was on 115k miles. The "hunting" was still there !! My X358 doesn't do it so clearly somebody did something, but won't release a cure for early cars;why I know not, but this is Jaguar after all.

 

My wife usually drives the car and I take it to gas it up, it learns her driving style.
I hit passing gear for a few seconds and it clears up.
Yes it the torque converter going into early lock up. It learns quick that I am driving....
Had the transmission software flashed while under warranty back in '05. Problem reoccurred in a short period of time.