Tens of thousands of wildfire evacuees in Los Angeles are now scrambling to find — and hold onto — temporary shelter, exacerbating the housing shortage in one of America’s least affordable cities.

With 92,000 people across Los Angeles still under evacuation orders on Monday, the displaced were scattered across Southern California, in shelter beds, hotel rooms, relatives’ spare rooms and friends’ couches, unsure about where to go next as extreme fire danger looms for yet another week.

The hunt for longer-term housing already has sparked bidding wars in some neighborhoods on the edges of the fires. In the ritzy Brentwood neighborhood adjacent to the Palisades fire, one real-estate agent suddenly got 1,000 applicants for a new rental listing. In Pasadena, a family whose home burned in the Eaton fire in Altadena said they were about to lose their emergency short-term rental where they have been staying since the fires to a family willing to pay $8,000 a month.

Some evacuees, like Lila King, have ended up staying in their vehicles.

Ms. King, 75, has been bouncing between motels and sleeping in her truck with her 40-year-old son since they were displaced by the Eaton fire.