The faucet in the kitchen with cold water starts up somewhat warm and then turns cold. The hot water is hot right away. I used to wait a little bit before it turns hot. A spot in my tiled floor is a little warm. The water meter does not indicate that I have a leak. One plumber told me I have a leak, while another plumber told me that I don't. I live in the Dallas area. We had pretty cold winter. Do I worry about this and get the opinion of a third plumber?
There is nothing about this condition that by itself suggests a leak. Common causes are your cold water pipes run near heating ducts or the furnace, or water from your hot water heater expanding back into the cold supply.
Likewise, a warm spot on your floor could be from ducting, a light below, the sun hitting it through a window, etc.
If there is a leak, sooner or later you will see signs of water - drips, stains on the drywall. If you do don't see any of these, I wouldn't worry.
Cold water starts off at room temperature because it is sitting in the pipes; gets colder as it comes from the ground outside.
Copper pipes are big heatsinks, so naturally your hot water lines could be heating the floor below (in addition to the adjacent cold water lines)
You could get those foam insulators for hot water lines if it bothers you.