Chrysler Repair: 2001 Chrysler 300M: overheating, coolant leaks, head gasket

Question
My car overheats after a few (maybe 5 or 6) city miles. It runs for a while at normal temp then the temp gauges jumps up fast to overheat. After it cools I check the coolant and it is really low. I have looked all over while it sits in my driveway running and dont see any coolant leaks. I have stuck my nose by the exhaust to smell for burnt antifreeze to see if I may have a bad head gasket but don't smell anything. I add more coolant and run it for a while and I hear the fan kick on but again after a few miles it's running hot and I have to add more coolant once the engine cools so that I can open the cap. The engine runs smooth and there is no knocking or rough idle so it doesn't seem like a cracked head but Im no expert so thats why Im asking what may be the problem. Thanks

Answer
If the coolant isn't boiling over, and if the oil isn't cloudy, and there is not other signs of a leak, then the coolant has to be going out the tail pipe. Let the exhaust gas condense on you hand after you first start it in the morning or after an overheat situation. That condensate is more likely to be noticed as a smell than the exhaust gas.
Roland