Examine hoses hot to check for soft areas. May need gloves. It seems possible if the hoses are soft could swell with heat and pressure and form a kink restricting flow. I had an OEM fuel hose "delaminate" from the inside and perforate, which would then swell when warm restricting flow. Talk about a perplexing problem. Also some safety bypass valve may be coming into play when hot to make you lose pressure.

I remember something like that happening to mine a few times. It was something to do with the helm that didn't cost any money to fix. Something was binding, only when hot out.
Good luck

Do the easy things first. Take the big nut off of the steering reservoir and make sure that your fluid is red. If it's not then it has broken down and needs changed. Also check it after running and make sure that it's not aerated. You need only hand tighten the nut after you check the reservoir.

If that's not it then it could be that your in-line filter is getting clogged up. I had to change out mine this summer. Typically you would hear the pump/pumps starving when you turn the wheel hard over if the filter was clogged. The filter is in an assembly that looks like this somewhere in the bilge. Your proportion valve under the helm could have something in it or be going bad. Then there is what has already been said - bad hoses or the cooler is clogged, loose belt. . Just a few ideas

Good luck.