Just a guess here, so hopefully someone here much smarter than me will chime in.

It sounds like a fuel or spark problem, like it is running really rich and has a carbon build up problem. It sounds like the fuel tables in the computer are wreaking havoc on the motor, either from bad oxygen sensors, or coolant temp sensor. Have you pulled the spark plugs to see what they look like? You say it runs fine on initial start up, then once it warms a little it runs rough, then once it warms more it runs fine. I would look at replacing the oxygen sensors, how many miles do they have? I would also pull the plugs to see what they look like, and replace them, maybe a cap and rotor too. I would also look into replacing the coolant temp sensor. Check for any trouble codes, do a complete tune-up, plugs, cap/rotor just to do it as the same time as the plugs, and definately oxygen sensors, and if you have a K&N or similar air filter I would clean it or replace it if it is not a reusable air filter. It also may be a vacuum leak problem, so I would check for vacuum leaks. Although you say it runs fine once it is completely warmed up, so it may not be that.
Once you have done all this I would get the car tuned on a dyno, so you can see what your A/F ratios look like, and fine tune fuel pressure and plug gap.
This also sounds a lot like the problems other people have had when using a C&L MAF. Their problems usually cleared right up after switching to a Pro-M, so maybe that is your problem too.
