My Mazda has a very rough Idling

Hey, I have a 93 mazda 626 lx 2.0 liters, automatic transmission, 140.000 miles when the engine is started the revolutions go up to 2000 ( without me pushing the gas. TACHOMETER then slowly slows down and stays under 1000, but it kind or doesn't stay steady, it is under 1000 of course but it doesn't stay steady, it does like if it is nervous. Moves trembling under 1000. IN PARK. At the same time the engine idles very very rough. When it is idling at the stoplight, I think it is the same when the engine is cold or hot. I let my mom borrow my car today and she called me soon thereafter and told me that at the red light the car felt like if she were riding a wild horse. I have felt that too sometimes. It is like if the engine wants to come out of the car :) well, I have changed the spark plugs, air filter and engine oil now. And the problem is still there. I have no idea what could it be. It you guys could give me some steps or something to stick up to. To follow the problem and pinpoint the cause. Here is some info.

the engine level is ok. I have never add more oil to the engine.(It stays full)

battery is ok.

transmission recently rebuilded.

spark plugs changed (but not cables)

air filter changed.

I have an engine check code which is 69 engine coolant temperature sensor (fan)

thank you