What heatsink?
The steel case would not make a good heatsink for disipating 10-15w
It looks like the rectifier has shorted and may have damaged the transformer.
Bit hard to tell friom the fuzzy pictures.
Wrong sort of fuse wire in this application. (constructive comment).
I bet the builder didn't supply you with a circuit either.
Put a 2 amp fuse in series with the mains supply.
Disconnect the two burnt wires and remove them entirely.
Turn it on.
Leave it on a minute or so.
If the fuse survives and nothing smokes, then replace the rectifier, and give it a better heatsink.
If the fuse blows, it looks like the transformer is fried also.
Super X3. 3600rpm. Sheridan 6"x24" Lathe + more. Three ways to fix things: The right way, the other way, and maybe your way, which is possibly a faster wrong way.