[Zeke]

No bare or green ground wire in the box means you have an old house with a non grounded wiring. Attaching the green wire to anything is useless in that circumstance.

For a short time in history, some houses were wired with conduit and a black and a white wire inside (simple circuit). The conduit was supposed to be the ground. You can test for the box for being grounded by using a meter between the hot and the box itself. If you get continuity, you can attach the new green wire to the box directly or by placing it below one of the mounting screws. (Note: this is not necessarily code compliant.)

Grounding has nothing to do with completing a normal circuit. It's a back up safety method. Your dimmer will get warm when the lights are set low. The potential energy not used when reducing voltage is converted to heat.

Use the correct lamps when using dimmers.