The oil pumps output, (flow capacity) is proportional to rpm. The flow requirements of an engine in good condition, (leakage through the bearings), should be fairly constant with rpm. So, the pressure should rise a little with rpm & then remain fairly constant as the regulator bypasses more or less oil to maintain it's set pressure. As pump output decreases due to wear, & engine flow increases due to wear, the pump can no longer can keep up with the engine flow requirements & pressure drops, especially at low rpm.
As you say, it would be normal for cooler oil to have higher pressure.
Possibly your engine was built with excessive clearances somewhere in there or the pump is not putting out as much as it should. Causes of low pump output could be, worn pump, leaks between pump & engine, or clogged pump intake screen. A remote possibility would be an air leak on the pump intake side.
It is a tough call. First thing I would do is verify the oil pressure gage with a temporary known good gage. True things could be better but the pressure isn't THAT low. I don't know how inclined you are to pursue the problem.
If you want to go further, pull the pan, Plastigage the rod & main bearings for proper clearances, (.002" max) check the oil pump thoroughly or replace it, & check for pump input or output plumbing leak possibilities. After all of this you may find that it didn't help much. The cam bearings can be a major source of pressure loss & are not easy to check.
I would just drive it until it gets worse or you can't stand to live with it anymore. Put a cooler on it if you wish, at least it will make the gage read higher.
There are folks on this forum who are far more knowledgeable about your engine than I. I'll leave it to them.
D