Nothing to do with cable or being melted or speedo fault, simply rear gear ratio does not match speedo gears in gearbox. Or by the sounds of it in your case, the tyre profile has been changed to something slightly taller than stock so it is going slightly faster than it thinks it is. Easy to fix if you want to, just depends on the combinations of above. Not sure they'd accept that excuse for speeding, more than likely they'd start to look around and find other faults.
Also, headers can be one thing with the speedo cable melting the sleeve, make sure the retainer is in place that holds it off as well, on inside of chassis rail.