1987 Jeep Wrangler 2.5 Starts fine but won't idle until operating temp is reached , I have to keep it at 2000 RPM or it will just die .

The following are the general instructions on the start of diagnosing any electronically controlled engine or transmission problem.

The engine and the automatic transmission (transmission control is only for automatics, engine is still computer controlled no matter the transmission type) in this vehicle are computer controlled and in most cases when a fault occurs a fault code is stored in the memory of the computer control module. There are exception to this, such as the Mass Airflow Meter and fuel pressure problems. What must be done is to have all the basic testing done such as a scan of the system for fault codes as well as a check with a live data scanner tool for engine functions that are not within range of normal, a trained technician is required to know what is correct and what isn't, then based on careful diagnostics done from a factory repair manual the correct part is replaced or the wiring repaired or the computer replaced (known as the PCM or ECM,ECU), which is very rarely the problem. Other basic checks must be done as well such as mechanical problems with the engine as well as engine state of tune and mileage on the engine. The transmission can have mechanical issues as well such as no gear engagement at all or a failed pump or other pressure related problems. Also engine mechanical problems can and do cause many drive-ability related problem such as rough idle and other symptoms.

Sounds like a coolant sensor problem. It signals the ECU for open loop, cold start rich, high idle, until warm up is reached.

It could be a combination of 2 things. A faulty MAP sensor itself or a bad TPS (throttle position sensor). It's not uncommon for a bad TPS to idle when the motor is cold but once warm, not idle fast enough to keep the vehicle running.

sounds like its starving for fuel,check your filter,then check your fuel pump is putting out enough pressure.

1. check for vaccuum leaks.
2. check for a check engine code
3. check the throttle body/butterfly plate for carbon build up.

you check for miss how is compression

The fuel pump is located in the gas tank and the filter is right in front of the tank on the inside of the frame. I have never worked on that particular throttle body, but if it has a throttle position sensor, that could be what your problem is.

Replace you fuel Injector pump and check for any bad or clogged injectors. make sure idle adjustment screw is properly set

normal for an engine to start at elevated rpm and then die back as it takes a few seconds for the ECM doing it's sensor checks and idle back to the correct idle speed
check the idle rpm with an external rpm counter as most in dash units are inaccurate at rpm lower than 1000
as for the temperature
If you have a climate control module, it uses a mixture of heater and ac to maintain the temperature that you have set
so check it for operation

2 things to check
your catalytic converter
your timing chain and gears