BMW Repair: 330i Shaking at Idle, coolant level, 2002 bmw 330i

Question
The thermostate seems to be working fine.  So the overheating could be the problem to the shaking of the car?  The shaking is very harsh and everything with the car seems to be moving.  The exhaust also seems to be misfiring.  Theres an excess of air then it ceases and after a few seconds begins again.  This could be from the overheating?  Thanks.
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Followup To

Question -
I have a 2002 BMW 330i with a manual transmission and 63,xxx miles.  When the car is in idle there is a really bad vibration that seems to be coming from the engine.  It starts subtle, but as I idle for a few seconds more the vibration gets worse and worse until I accelerate.  When I accelerate it seems to go away, but comes back when I stop and put the car in neutral.  

I'm not accelerating very fast because I'm being very cautious with the car, but when I drive, I randomly pull over into gas stations every 15 minutes just to check the car and the temperature of the engine just seems to be really high.  There was also a hint of white smoke when I opened the engine, but it seems to have gone away.  

I took the car for an oil change today, but there is no change to the violent vibrations of the engine when I'm in idle.  What could be the cause of this vibration and abnormal temperature of the car?  Thanks.  John

Answer -
John, how is your coolant level? You might have the fault memory read out. You need to solve the overheat immediately. These All Aluminum engines do not respond forgivingly to overheats. I would suspect a faulty thermostat or electric fan not working. I also think the overheat may me causing the erratic idle. Pressure check the cooling system if it was low on coolant. Make sure lower radiator hose gets hot and pressurised.
-Evan

Answer
John is the motor actually hot when the shaking happens? Or does it happen when it's cold too? Overheating usually doesn't cause violent shaking. You may be looking into two separate issues. Electric fan comes on? Does the viscious fan clutch engage and pull a significant amount of air when the motor is very hot? Again Coolant leaks? Where do you notice the excess of air? Check the intake boot for leaks down toward the throttle body. Check the little idle valve hose that branches off from the main intake hose. Also crack open the oil filler cap just a little while the engine is running. Is there a large vacuum or a strange noise when you do this?
-Evan