Eru

Just to put it here, coils are made of wire ( yeah, pretty obvious) that are isolated by some sort of varnish, instead of a plastic based insulation like most other electric wire/cable..
If its not shorted to any other wire (be really careful when diagnosing a psu) you could apply some nail polish over the burnt area, a couple layers could do.
Keep in mind this is only my opinion and I am not an electronic engineer... I got a diploma in industrial electro-mecanic.. I would advice you only look at repairing this psu if you can't afford to buy a new one.

When you have finished your repair may one suggest you use a PSU tester rather than your rig to see if it works, one would not like to damage any other components.

Its a Thermaltake Toughpower Gold 750W
 
 
 
Warranty is long gone.
Its been sitting inside the box for around 2 weeks now so I'm sure its safe to handle. Will do an operation   on it then report back here later. Thanks for the replies!