The damaged plant near San Clemente is likely to remain offline until at least the end of August. Investigators are looking into excessive wear in tubing that carries radioactive water.
If a heat wave hits while the twin-reactor plant is offline, officials say rotating blackouts are a possibility in South Orange County and San Diego.
Edison has been scrambling to find replacement power as a precaution, including taking the extraordinary measure of restarting two natural gas fired plants in Huntington Beach.
The last rolling blackouts hit Southern California in 2001, leaving thousands in the dark. Edison is encouraging customers to start conserving now.
San Onofre has been shut down since January when the Unit 3 reactor was shut down as a precaution after a tube break. Traces of radiation escaped at the time, but officials said there was no danger to workers or nearby residents.
Southern California Edison said in a statement that the company plans by the end of July to submit a plan to federal regulators to restart the Unit 2 reactor, but a proposal to restart either reactor must be approved by the Nuclear Regulatory Commission, and that review could take weeks or longer.
Edison would forewarn customers before implementing any rolling blackouts.
The Associated Press contributed to this report.