Welcome, Alex.
I'm just going to rattle off a couple quick ideas for you to check. Our ZXs differ in some ways, especially when it comes to the "brain," but we share enough components that some of these might help:
Check all of your vacuum hoses, they tend to dry rot and become brittle. You won't really be able to tell just by looking at them, but if you pull them off the bad ones should be pretty obvious.
Check the rubber boot between the Air Flow Meter and the throttle body, as well as the hose that goes to the auxiliary air regulator.
You might also want to check the PCV bit located on the driver's side of the block, about in the middle. The rubber hose that is attached to it may be leaking in air, and is a pain to remove if bad. Be careful with this piece, you really don't want to have to replace it.
There is also a thumb screw on top of your throttle body that you could adjust, but since the car idles down after a bit, I doubt that this is the problem.
You might also want to check all the electrical connectors on your thermostat housing. If the thermotine switch isn't sending accurate info to the brain, your car may try to compensate for what it feels is a cold start situation. Even if this is not the culprit, it's still a good idea to clean these pieces of corrosion.
I'm sure I've missed some things, but these points should help narrow down the problem.
Let us know your results.
Bookmarks