Since you are in Los Angeles, it's not like she's at risk of exposure outside when you are away for a few hours. It rarely gets below 40 at night there, even in the middle of winter --and it's often considerably warmer (the average low in Dec./Jan is 49!).
Still, if you want her to go in the dog house when you aren't home, get her to go in when you are home. Acclimate her to it like a crate -- reward and praise when she goes in. Also, try place her food bowl inside it for a few weeks and let her eat inside it, with you standing nearby, so she gets used to thinking of it as her space.