I'd like to take some space for myself on this thread and clarify a few things about the model C64C:
There are actually 2 versions of this computer.
The Earlier (let's call it C64C v1.0)
Which did/does have a metal shielding (I used to own one back in 1987-92) it had sort of metal clips touching the chips with thermal compound to double as a heatsink as well as a RF-shielding (!)
This version is more likely to be identified externally with the keyboard itself because the keys also have printing on the front of the keys, not just the top, and the printing on the control-key says CTRL
It has a 6502 processor and 6581 SID
The Later (let's call it C64C v2.0)
This was the cost reduced model (as the manufacturing processes developed and certain chips were cheaper than the ones found on earlier models (revision E motherboard)
It has a foil coated cardboard as a shielding.
The processor is a model 8500 (virtually identical to 6502 in any way) The SID chip had changed to 8580
This model can be identified also from the keyboard which had ALL the print on the TOP of the keys.. also a serial number above 1.000.000 should indicate a later version c64c..
The C64C i have now has all of those v2.0 identifications, and the serial is HB4 1325712E