Hyundai Repair: P1372 and P0303 Error Codes Randomly Occured, hyundai elantra, crank sensor

Question
2001 Hyundai Elantra, Car had a bad AC recharge previously. We drained and recharged the system, and ac worked great. 4 days later the car starts to smoke and gets a check engine light. When I get the car from my friend the day after it smoked I was told the engine light was gone and the engine bay was cleaned and the car is fine. I proceeded to drive the car to get the AC leak test completed, which was part of our recharge. As I am driving no more than ten minutes, at approximately 70mph, the car over heats and no more than 5 min later the engine smokes, and following the check engine light turns on. My mechanic evaluates the smoking and says the radiator is cracked, mind you no check engine light when he looks at it. I replace the radiator properly, only to find the cars AC and Heat both dont work, again as they need when it was over heating, and I have a check engine light with 2 codes P1372 and P0303. We clear them and they come back, 3rd cylinder misfire is what the code states. Car sputters and does not run strong has a hard time idling as well. Can not make the connection between all 3 items, any help would be greatly appreciated. One other mechanic said it was the head gasket but the car runs clean no white smoke from the tail pipe or mixing. Could it just be the Crack shaft position sensor or a bad coil pack, ie something electrical or is it physical damage??

Answer
Most likely, the A/C is a separate issue.  While the A/C won't work if the car is overheating, it should at least blow cold on a cold start.

As for the misfire on cylinder 3 (P0303) and crank sensor code (P1372), it's hard to say.  This engine is very sensitive to overheating and will easily warp the cylinder head.  On the other hand, all the performance symptoms as well as the misfire code can be caused by a faulty crank sensor.

This leaves you at a crossroads as to how to diagnose.  You could replace the crank sensor and see what happens.  Or you could do a compression test to get an idea of the general health of the engine.

As for the lack of heat, you may have an air pocket in the cooling system or it may not be completely repaired.  If, for example, the thermostat were stuck shut causing the pressure to build and crack your radiator, you'd still have the problem that you have no coolant flow, resulting in no heat.

Unfortunately, considering the overheating, my inclination is that you're more likely to need a cylinder head than any of the minor repairs I've suggested.  But the only way to find out is to check the cooling system, compression, and crank sensor.