If the "Ground cable" is overheating, you better find where the short circuit is in the machine.
Now if you are talking about the work lead overheating, I would ask the question, "Why is the cable over heating? Is the cable undersized or are the connections loose or heavily oxidized?"
Usually, once the work lead is over heated, the connections become oxidized, making the heating problem more severe. It is like a snowball rolling downhill. The thing is, you can't make it worse than it is once the insulation has melted and burned off. The upside is the insulation will not have to be removed when it is sold to the scrape dealer.
Al
The problem is the electrical resistivity of copper cable increases with the increase in temperature, this will produce more heat and so on and so forth. After several overheating episode, the copper has lost some of it's cross sectional area and so is less efficient and the conductivity drops but the resistance increases.
The easiest way is for you to answer your own question. Get a new section of copper ground cable of a given length, say 20/30 feet and measure the resistivity with your bog standard electrical multi meter or a dedicated Ohms meter. Then get 20 feet of your burned out cable and measure the resistivity. The difference in the two figures will show the effect and the loss of efficiency. Bear in mind, this would ideally need to be done whilst welding was taking place using these ground cables.