Power steering is very stiff at idle

The power steering pump looks like a version of the German-made "ZF"-style pump used on early 1990's Chrysler products. They developed this same symptom, but heat was not a factor with those. They lost power assist at idle at all temperatures. The pump uses fiber vanes that wear down over time, then they become less efficient and there is some leakage around them.

There is two clues to look for. First, this only occurs at idle speed. At slightly higher speeds, the pump produces sufficient volume to run the steering gear in spite of the internal leakage.

The second clue is when power assist is lost due to leaking Teflon seals in a rack and pinion assembly, you will always lose power assist to only one direction at first, then the other direction a few weeks later. Increasing engine speed does not help when the leakage is in the rack assembly, and that problem clears up when the power steering fluid warms up. Often the power assist returns in as little as ten to fifteen seconds at first. As this problem progresses, it takes more and more minutes each day before the power assist returns. It might take ten minutes before you get power assist when turning left, for example, but by that time you will have also been losing power assist to the right, but that will return sooner.

To say that a simpler way, when the power assist is lost due to the rack and pinion assembly, the symptoms will differ between turning left and right. When there is excessive internal leakage in the pump, the direction you are turning does not matter. You will lose power assist both ways at the same time, and it will return both ways at the same time.

Given the additional variable of temperature, do not overlook something as simple as a slipping drive belt for the pump. Tug on the serpentine belt, (when the engine is not running, of course), and watch the spring-loaded tension-er pulley move. It should move smoothly, and pull the belt tight again when you release it. It is not uncommon for the tension-er to get rusty and tight in the pivot bolt, and fail to keep the belt tight. Often you will also observe a chirping or belt squeal, and or the lights dim a little and the heater fan motor slows down because the belt is slipping over the generator's pulley.

Check out these articles for more information:

https://www.2carpros.com/articles/power-steering-problems

https://www.2carpros.com/articles/how-to-replace-a-power-steering-pump

When you flush a system, it is always full. You are just putting new in to push some of the old out.

When you do a more-common drain and fill, it is not possible to completely drain the entire system. You will empty the power steering fluid pump, reservoir, and any hose you disconnect at the steering gear. The rack and pinion assembly itself holds a lot more fluid than what is in the reservoir. That fluid in the rack does not drain out.