[wiswind]

Rough idle on warm start could be from coolant leaking into the intake after you shut it down.
I had that with mine until I took care of the lower intake manifold gaskets.....
The coolant is then drawn into the engine....causing the rough idle.

The only way that I see a connection between a coolant leak would be, again, with leaking lower intake manifold gaskets......
Mine caused a buildup of gunk in the lower intake.....including on the IMR butterflies for cylinders #1 and #4, which is where the leak was.
Maybe the buildup is bad enough to cause the plate to hang up, causing the shaft to not move the full expected travel distance.

The heat issue could be caused by air getting into the cooling system.....which will cause the overheating and / or no heat issue.
Take note that leakage from another location, such as the front cover (aka timing cover) or even a loose hose clamp will cause the same issues of heat and engine temperature.
IF the hoses are original.....I would give them a very careful inspection.....including the heater hoses, and the short elbow hose that is on the pipe that comes out from the top of the water pump....goes toward the firewall.......the elbow is the one that turns toward the radiator...connects to a pipe that goes into the center of the lower intake manifold.

Just out of curiosity, you might check and see if you have low speed fan function.
With the vehicle in Park, turn on the A/C, and raise the hood to see if the fans are running.
If not.....it could be the low speed dropping resistor for the radiator fans.
I have pictures of that in my pictures.