2001 Ford Focus SE strange "warm weather" problem

Thank you for taking the time to look at my post. I will start by describing the problem, followed by what all I have done and had done to the car.

Problem:
First of all, in all weather, at all times, my engine idles rough. The car will drive fine, gets somewhat poor gas mileage, and is a little less on acceleration power. Now the strange part… When in hot weather, after a night of sitting, the car drives fine initially for a while. If I am driving the car for any more than a half hour or 45 minutes, and the temperature gauge is at normal operating temperature (a little past halfway on the gauge), the car at any time can all of a sudden lose engine power (more likely to happen if I am idle at a red light or stop sign). All of a sudden when not pressing on the gas, the engine shudders dramatically. I press the gas, the RPMs shoot high but there is no accelerating power. It will creep up slowly as I leave my foot pressing the gas to the floor, but on flat ground will usually max out at about 30-35 mph. Sometimes if I keep coaxing it for about 5-10 minutes, it will snap out of this mode for a few minutes, and then happen all over again. Occasionally, but not often, if the car is running in this mode and i stop at a light or stop sign, the engine will die. Also if at any time I drive my car somewhere and it reaches normal operating temperature for more than a few minutes, when I turn off my car, then come back and turn it on, it immediately starts up in this mode, the engine shuddering dramatically when I turn it on. Sometimes, if the weather is colder or cooler, and not blistering hot, I can pop the hood for about 30-45 minutes, let the engine cool, and it starts up ok and runs alright for me for me usually long enough to reach my next destination.

Some history:
I had a pretty bad oil leak for a while and the mechanic replaced my oil pan, fixing that issue. While the oil leak was occurring, i kept oil in the engine for the most part, and the engine started idling rough after a few weeks, but never had this issue. This all of a sudden occurred one day in the hot weather last summer, a few months after the oil pan replacement.

Work Done:
I have 145,xxx miles on it.
The timing belt and water pump was recently replaced.
I have replaced the Idle Air Control Valve.
I have replaced the Mass Airflow Sensor.
I have replaced the crankshaft position sensor.
I have replaced the thermostat.
The thermostat housing recently cracked as well so I had that replaced.
I have checked for vacuum leaks.
Sometimes (not all the time) when the issue occurs the Check Engine Light comes on. Each time the mechanic says the code comes up as an engine misfire, nothing else.

Some suggestions people have given:
Replace Coolant Temperature Gauge
Replace bad O2 sensor(s) - However no code is being given for which O2 sensor
Check Catalytic Converter

I hope that covers it. If I remember anything else I will post it.