I find the problem is more evident when the car's HOT.
I guess that does point to either "real knock" or something mechanical (rods, bearings, or external to the engine metal to metal contact etc). It also suggests to me that it's not lifters either. Most times lifter noise clears up with oil temperature.
It might be possible that you have a wiring problem (poor ground) that will induce more noise with increasing temperature (electrical noise is proportional to resistance and temperature). (Kind of a stretch because the induced noise should be white noise and I *think* the ECU windows the noise in frequency and bases it's knock detection off the background noise threshold outside that window?...)
This problem is well beyond my realm of experience.