is the steering rack shot and seizing up?

 

No. When it is stiff, it is stiff evelyn and not sticking, if you mean this by "shot" and "seizing".

 

Did you replace the fluid with Dexron III compatible ATF?

Maybe one of the hoses is getting kinked as it warms up and preventing fluid flow.

Maybe the belt starts slipping on the pump when it warms up.

 

Maybe one of the hoses is getting kinked as it warms up and preventing fluid flow.

I had a similar thought, but I was thinking that maybe something is expanding with heat, impeding fluid flow?

 

the pump maybe having issues, there is a bypass in there when the pressure gets to a pre-set point... I would find someone who also agrees, as I don't want you to work on something that maybe good. Pumps can be expensive, and a rebuild is a pia for those that do not do mechanical work. Rebuilds are ok.... but still not cheap. I honestly do not see it as a rack problem....

 

Not a bad idea to check the pump. I have a friend who has the same car with a well functioning pump, and I can ask him to have his power steering pump... I know it is a headache, but we are having fun troubleshooting our cars.
I will report back on this

 

So, I checked it with a new power steering pump, nothing changed. Checked for kinked hoses and built slipping, both were ok.
I went through another check, the mechanic told me to park the car under direct sunlight for 30 mins, and then see whether it gets stiff or not; I did so and it got stiff. The mechanic concluded that I it is something in the intermediate shaft which expands with heat and causes stiffer steering wheel. Its changed and so the problem is solved.

DrZ and Pete Suhman were right with the diagnosis, however, in a different location. Thanks to both