* Head Gasket Failure: This is the most probable cause. Overheating can warp the cylinder head or crack the head gasket, allowing coolant to leak into the cylinders. Coolant in the cylinders creates a milky, foamy substance that burns, producing the black smoke. The shaking is due to the engine misfiring because of the diluted fuel/air mixture.
* Cracked Cylinder Head: Similar to a head gasket failure, a cracked cylinder head allows coolant into the cylinders. This is often accompanied by other symptoms, such as loss of coolant and pressure in the cooling system.
* Damaged Engine Blocks: Severe overheating can crack the engine block. This is less common but equally catastrophic.
* Internal Engine Damage: The extreme heat could have damaged pistons, piston rings, or connecting rods. This would explain both the black smoke (due to incomplete combustion) and the shaking (due to mechanical imbalance).
What to do:
1. Do NOT start the car again: Further damage is likely if you continue to run the engine.
2. Check the engine oil: Look for a milky or foamy consistency. This strongly indicates a head gasket failure.
3. Check the coolant: Inspect for signs of oil contamination (looks like chocolate milk).
4. Have it towed to a mechanic: This is not a DIY repair. A professional needs to diagnose the problem correctly to avoid further damage or potentially dangerous repairs. They'll likely need to perform a compression test and possibly a leak-down test to pinpoint the exact source of the problem.
Ignoring this problem will lead to significant and expensive engine repair or even replacement. Getting it checked out immediately is crucial.