any luck sorting your car out?
when Lamba sensors go bad it causes the engine not to idle smoothly and rev up and down use more fuel than normal. Engine will do this running hot or cold as the ecu is getting the wrong readings from the Lamba sensor
The engine will not run good if you disconnect it. more likely you need to change the temperature coolant sensor and clean the throttle body with carb cleaner also take the spark plugs out clean them with a wire brush as they could be sooted up if engine is running rich.