It sounds to me that the choke is closed when the engine is cold so starts and runs, but does not open fully when warmed up so stalls out the engine. Check the operation with the old air cleaner installed, then let the engine cool down and compare that to then operation with the new cleaner installed.
The new cleaner may be creating less vacuum to the heat riser so it's not warming up the choke thermostatic spring as fast as with the old cleaner. This can be checked with a vacuum gauge. Connect a spare length of hose to the old cleaner vacuum port, install the cover, start the car up and test it. Then do the same with the new cleaner.
To adjust the choke a couple index movements of the choke thermostat towards "rich" may be all that is required. There is a chance however that you'll need to upgrade to an electric choke.
2005 4.0 MT dual exhaust GT mufflers GT suspension and wheels