Ford Mondeo Problem 2.0L 4 cylinders

When it's cold, it doesn't have a problem, but after driving it for a while (15-20 minutes), it has trouble idling smoothly (without accelerating). It shakes a lot, to the point of stalling. I used a scanner and it gave me codes P0351 and P0352, related to the ignition coil. I checked the coil wiring and it seems to be fine. This is the coil www.ecplaza.net/ecmarket/imageview.asp?i.../adashao/5266634.jpg .

Coil pack resistance data:
Primary 1: 1.3 Ohms,
Primary 2: 1.3 Ohms,
Secondary 1: 10,400 Ohms,
Secondary 2: 10,540 Ohms.

Additional comments:
The problem started after driving on the highway.
The car can restart after stalling.
If I accelerate a little (over 1200 RPM), the car runs fine, without vibrations. The problem occurs at low speeds (without accelerating).
The coolant temperature when the problem occurs is 216°F (102°C).
The IAT sensor temperature is 136°F (58°C).
The engine RPM drops to 714 (normally it's between 900-950).
The MAP sensor reads 15.9 inHg.
The spark plug wires were replaced 2 or 3 months ago.
I also see that it's consuming coolant, or rather, water. I've already inspected for leaks, but there don't seem to be any.

As a final note, I tuned up the car a week before going on the road, changing everything (spark plugs, oil, filters), and I also cleaned the injectors with a fuel injector cleaner. It ran well until just before the road trip.

What do you recommend? What else should I check?

I would check the IAC valve, or stepper motor; this controls the idle speed and if it's faulty, it tends to stall the engine due to lack of air.

What do you mean by stepper motor?

I already cleaned the IAC valve and the MAP sensor, but the problem persists. How can I test the IAC valve? By applying voltage?

Karma, the problem you have is the fuel pump. This happens to most Mondeos of that year. Put a pressure gauge on it, and when it starts to fail, the pressure will most likely drop. If it does, then it's the pump. If it is the pump, don't buy a cheap replacement; buy the original part. If not, then buy the whole pump. Make sure to clean all the hoses and blow them out with compressed air. Good luck.