Let’s see what it says here about the 1.6/L4 … hmmm… it appears you have a PCV, but no EGR (as you already said), a single 3-way cat (for CO, HC, and N), EI/ECITS spark control, and 2 heated oxygen sensors. Have you replaced the O2 sensors yet? Not suggesting that you do, but wondering if you have already.
You say you aren’t getting any codes, but that may be b/c you’ve cleared them by disconnecting the battery, and they haven’t had a chance to return yet. Did you in fact clear the codes or disconnect the battery? The problem you are having is so severe that it’s hard to imagine there wouldn’t be at least one code thrown.
Ok, well not all the data available yet, with no codes reported at all, so time for some guess-work. It sounds to me like one of these four would be where I’d start with my suspicions for the guilty party
- O2 sensors on the fritz
- Fuel pressure problem
- Exhaust leak prior to the O2 sensors
- Spark problem, quite possibly the crank sensor, but could be the ignition module too
The reason I say these 4 is that all four typically exhibit temperature related symptoms. While it could be other things, for example I wouldn’t expect such extreme temp sensitivity for the MAP or TPS.
Unfortunately none of these are particularly easy to test without the proper testing equipment & shop manual info. hmmmm … well , you could get a length of garden hose I suppose and use it to probe for a small exhaust leak prior to the O2 sensors. It would be making a putt-putt or pop-pop sound near where the leak is emitted. A cracked exhaust manifold isn’t at all an uncommon thing, esp with these smaller engines. The crack can be closed when the engine is cold, then open up as the engine warms.
& you could test for spark at the spark plugs when this is occurring. There are in-spark-plug-line gadgets you can buy at auto parts stores that make this relatively simple.
Checking the PCV is simple so you might as well try that too.
This kind of drivability problem is often better solved by someone experienced and with the car’s scan tool. Like the dealership shop. I sense you don’t want to go that route. But you might could be dollars ahead by considering this, at least have someone with the proper tools and experience do the diagnosis, then you do the parts replacing.
Sorry, that’s the best this amateur DIY’er can offer up at this point. Best of luck.