The amount of dissolved CO2 is a function of pressure and temperature. There is also a pretty big difference between 6 PSI and 12 PSI. For a typical beer at 40 F and 10 PSI, your "volumes of CO2" will be about 2.3. For a similar CO2 content at 70 F, you need to maintain a pressure of about 30 PSI. This means open the CO2 valve, set the regulator at 30, connect to the keg and wait. According to the tables, this will give you about 2.3 volumes of CO2 once everything comes to equilibrium, which should take maybe a week. After a week, disconnect the CO2 inlet and put the keg in the fridge with nothing attached. Theoretically, once everything chills down to 40 F, the pressure in the keg will have fallen from 30 PSI to about 10 PSI.
You can view the carbonation table at http://sdcollins.home.mindspring.com/ForceCarbonation.html