Neautral wire overheating

I'll point out that basic electrical theory states that the current will be the same at all points in a circuit like that- the hot is carrying the same current as the neutral, and the current is the same at the plug, outlet, cord, etc. It is just a bad connection at the point of failure, and once it has overheated, you need to replace everything that got hot. The only thing a longer cord would do is drop the voltage a bit, causing just the air conditioner to draw more current, but it will not draw enough to burn up the wire- a breaker would trip far before that happened due to an over current situation.