How old is the PS fluid in there, in years and mileage? If it's the factory fluid on a 4th gen, it's way past time for a fluid change. Consider using power steering fluid rather than ATF Dexron III, based on this:
How to make your Toyota Last Over 300k Miles without Major Repairs - YouTube (skip to 13:37 for PS fluid comments)
My '07 has 276K miles on it, with PS flushes over the years I've tried Castrol MaxLife ATF, Valvoline Dex/Merc, and finally settled on LubeGard Synthetic Power Steering Fluid. The ATFs were fine, but it had a groaning sound on cold startups below approx 40deg F. Louder as it got colder.
After viewing the guy's video linked above and seeing reasonable evidence of his claimed experience and certifications, I flushed in the Lubegard fluid and the cold groan is gone.