I think it's because of the sharp edge, not because of the heat from radiator.Is the cable being worn from the sharp edge of the radiator or is it from the heat melting it from the hot radiator? I checked it after riding and it seems like the heat could be melting the cable.. Either way needs to be addressed.
But to be sure you'll protect the clutch cable for heat and for abrasion too, you can use a PET cloth wire harness tape for high abrasion protection and high temperature resistance (see this link for more details).
You can buy it from ebay for $8.