NEW YORK -- The competition to buy a small coffee chain is getting steamy, with Starbucks and actor Patrick Dempsey among those vying to become its new owners.Starbucks Corp. confirmed that it is participating in a bankruptcy auction Thursday to buy Tully's Coffee, which has 47 company-owned locations in Washington and California. Tully's filed for Chapter 11 bankruptcy protection in October. Dempsey, who gained the nickname "McDreamy" on the TV show "Grey's Anatomy," also said last week that he wants to rescue the chain. Baristas Coffee, which operates a chain of drive-thru espresso stands featuring female employees in skimpy outfits, has also expressed interest.The auction process is not public. The outcome is expected to be filed in court Friday.