The 2 aren’t necessarily related. You don’t mention how warm the water is. I get something similar with my cold water. In my case, it’s the fact that there are runs of cold water pipes in the walls, between where the water comes into the house and the faucets. The water in these pipes, when it sits, warms up to room temp. When I turn on the cold water tap, the water feels warm, until the pipes are emptied, and when I start getting water that was shortly before in the water main, it is much cooler.
Except that I’ve lived in this house for 4 years and this has never happened before now, so it seems nearly certainly related
Do you have a slab or a crawl space? If it’s a crawl space could you have heat tape on your pipes in case they freeze? That could be stuck on.
Has anyone been to the crawlspace to check it out?
Where in California are you. Is geothermal activity a possibility? Do you know of any Hot Springs nearby?
I don’t think I’ve seen this asked -
Do any windows put sunlight on the area for an extended period of time, particularly any windows with any lensing effect?
So we had the leak detection people out this morning, and it’s a leaky pipe under the slab (no crawl space). Fixing it will require jackhammering the slab. So another $750 on top of the $250 to find it. Ah well.
I had a leak in the slab repaired for much less by a plumber who works for himself. There may of course by licenses and permits involved for you, but it may be worth checking out. He chiseled the pipe out of the slab.