The coil should have a hot lead coming from the ignition switch thru the pink resistance wire. The exception is that the coil gets a full 12 volts from the "IGN" terminal on the starter solenoid when the starter is engaged.
Whether the case is grounded or not by the mounting clamp would have no effect on the coil heating or not heating.
If the coil is running excessively hot (you can't hold you hand on it hot, you could have internally shorted turns in the coil windings. It could also get hot if it has 12 volts applied because the pink resistance wire has been by-passed somehow.
The other side of the coil goes to the distributor points and is grounded when the points are closed. The spark occurs when the points open.
First check the voltage at the primary terminal of the coil with the engine running. It should be reduced to around 7 volts by the pink resistance wire. If you see a steady 12-13 volts, the resistance wire has been by-passed.
Are you talking about a repo yellow top coil? If so I think up until recently the older repo's weren't that good. I have heard from others as well as my own that went bad. Mine was about a year old and died in the middle of an intersection one night. If you read some of the vendor catalogs they now list them as "new improved" so that tells me the older imported repo's had problems. I believe it's do to heat. So I went for reliability instead of looks & bought a Pertronics 40K volt coil and just heated their label off it. Been fine since.