Hi, Look I'm just an apprentice Z owner and until one of the more knowledgable owners see this thread I'll offer up this:
Do you have any DTC codes?
If yes, did you look them up?
Did you put a scan tool on the data port? What did the scan show?
I own a 90 and when my primary injector coils started shorting the imbalance in cylinder output due to the lack of fuel caused my car's dual mass flywheel to start rattling. It made the car sound like a diesel...the noise was hurtful at times. It had a big miss or skip, and the hotter the motor got the worse the miss got. I learned the reason is that once the injector coil starts to short it will only get worse. The car ran almost fine when it was cold...you had to listen very closely for the miss from the bad injectors but after it reached proper operating temp...man did the miss show up! I used a scan tool to "view" what the motor was doing in "closed loop", by seeing the results of combustion in the O2 sensor numbers(cross counts & milivolts) and the block learn numbers & integrator numbers you will see that combustion is not normal. I'm not saying that this is your particular problem. The only reason I jumped in is because you said when it's cold it's not audible & when it gets warmer it starts to become evident & it seems the hotter the motor gets the more the miss & noise becomes evident.
Do you have a Helm manual set for the car? If not they are a very worth while purchase...Helminc.com...those are the genuine GM service manuals for the ZR-1.
Tom