2006 Crown Vic misfiring

The plug wires may be bad , Is there a fuel line getting warm any where on the motor or near the exhaust manifold ? Any customizations ?"

Vacuum leak when it gets warm, injectors going out of specs when warmed up, sensors misreading. What does live data show?

These have plastic intake manifolds that tend to crack. There's also a good possibility that, if the spark plugs have been replaced one or more of the spark plug holes are now striped and need to be repaired using a Helicoil. But judging by your symptoms, I'd suspect a cracked intake manifold first. Jim