To add to Keoke's comments, be sure to mark and disconnect the low tension wires from the coil when you make the resistance measurements. You don't want anything else on the circuit altering your resistance measurements.
In '65 your car would almost certainly have used a standard, 3 ohm coil. IF the parts store sold you a coil for ballast ignition, and/or likewise if VB accidentally sent a ballast ignition coil, it would be passing too much current and would get hot. However, I'm not sure why this would prevent the car from starting. Usually what it does is cause the premature death of ignition components.
I looked at the listing at VB and it says that the 8-627 is a screw-on coil which would certainly mean it's a standard 3-ohm unit. Now for a question, since it's a screw on type coil, are the low tension terminals still marked SW and CB or has that changed to (+) and (-)?