1. Idle Air Control Valve (IACV): The erratic idling strongly suggests a problem with the IACV. This valve controls the amount of air entering the engine at idle. A faulty IACV can cause hunting idle (fluctuating RPMs). Cleaning it (often involves removing and spraying with carburetor cleaner) is a relatively easy first step. If cleaning doesn't solve it, replacement is likely needed.
2. Coolant System Issues (Overheating): The overheating after 10 minutes is a serious problem. Several things could cause this:
* Low Coolant: Check the coolant level in the overflow reservoir. If it's low, you have a leak somewhere in the system (radiator, hoses, water pump, head gasket). Look for visible leaks.
* Faulty Thermostat: A stuck closed thermostat prevents coolant from circulating properly, leading to overheating.
* Radiator Issues: A clogged radiator (due to debris or corrosion) or a faulty radiator fan (not turning on or insufficient airflow) can prevent proper cooling. Check the fan operation (should turn on when the engine reaches a certain temperature).
* Water Pump: A failing water pump won't effectively circulate coolant. You might hear unusual noises from the water pump if it's failing.
* Head Gasket: A blown head gasket is a serious issue allowing coolant to mix with oil or enter the combustion chamber. This could also explain the erratic idling if coolant is entering the cylinders. Check for white smoke from the exhaust (indicative of coolant burning) and milky oil (coolant in the oil).
3. Mass Airflow Sensor (MAF) Sensor: A faulty MAF sensor can provide incorrect air/fuel mixture readings to the engine computer, leading to rough idling and potential overheating if the mixture is too rich (burning more fuel and generating more heat).
4. Throttle Position Sensor (TPS): A faulty TPS can also cause erratic idling and poor fuel mixture, contributing to overheating indirectly.
5. Vacuum Leaks: Small vacuum leaks in the intake manifold or hoses can disrupt the air/fuel mixture and lead to erratic idling.
Troubleshooting Steps:
1. Check Coolant Level: This is the most urgent. Top it off *carefully* (engine cool!) if low, but don't drive it further until you find the leak.
2. Check Radiator Fan: Make sure it operates when the engine gets hot.
3. Clean the IACV: This is a relatively easy fix that often solves idle problems.
4. Inspect hoses and connections: Look for cracks, leaks, or loose clamps in the cooling system and vacuum lines.
5. If still overheating after addressing the above, consider a pressure test of the cooling system to pinpoint leaks. This usually requires a specialized tool.
6. Consider professional diagnosis: If you're not comfortable working on the car yourself, take it to a mechanic. They have the tools and expertise to diagnose and fix the problem efficiently.
Important Note: Overheating can cause significant engine damage if not addressed promptly. Do not continue driving the car if it's overheating. Let it cool down completely before attempting any repairs or further driving.