Hi, welcome to JustAnswer!. This is Ed.
If I had to tie your overheating event to the problem you're seeing now, I'd expect it to be an ignition spark-shorting sort of affair.
When the engine overheated, chances are good that coolant got sprayed all over the underhood compartment. Coolant (glycol) is a decent electrical conductor at the voltages ignition systems operate at and if it reached the coil pack or plug wires, it may have exposed a weakness in your ignition system that was there previously, but wasn't being exploited. Glycol doesn't evaporate readily, so its effects may last quite some time.
One of the problems we're faced with is that we don't know exactly what your hesitation or popping problem is being caused by, but my suspicion is that it's all within the secondary ignition system.
The engine uses a coil pack - a pair of coils - that supply power to the four cylinders. Each coil fires once per revolution, providing spark to the cylinder pair, but at different times during their cycles.
Spark occurs during one cylinder's TDC power stroke, while at the same time a "waste" spark is shot through the companion cylinder on its overlap cycle. If the primary spark fails for any reason, you will have a very combustible mixture left in that cylinder which can be touched off during the waste spark event, which will create a backfire through the intake manifold. A loud <POP>.
Access to the coil pack and plug wires is poor on the 2.4 PT, requiring that the upper intake plenum be removed to inspect the center two plug wires. You might be able to inspire spark to leak from the coil pack (if that's the leak source) by selectively spraying some Windex or similar water-based fluid directly on the coil or plug wires. Barring that, I'd have to pull the intake off and check for glycol or signs of flashover misfire in the plug wire ends buried deeper in the cylinder head.
Eventually you'll get a MIL illumination and misfire trouble code recorded to tell you which (or how many) cylinder(s) are involved. For now, we're flying a bit blind, but I figure this is the most logical cause.