Let's look at this realistically... no hypotheticals....
You might think from the names of the modes in TV menus that "standard" or "normal" or some other average sounding name would be the right choice. But when you actually measure those modes, your result is ALWAYS far too blue, typically producing color temperatures in the 9000-11,000 range.
This has been the way TVs have been delivered for generations. It's primarily so when the TV is on a wall with 50 or 100 other TVs, it looks as bright and punchy as every other TV up there. A calibrated TV in one of those walls would sell zero units because the pictures of all the others is so hyped that the CORRECT TV would look boring.
The names of the settings in the TV menu really have NOTHING to do with hour accurate the particular mode is, they are just names. They could just as well have called the modes Bob, Dinosaur, Chevy, Chardonnay, and Atlantic. Those terms would be just as descriptive as the names the manufacturers chose to use.
So lets say the TV has 5 modes... Dynamic, Action, Standard, Warm 1 and Warm 2. If Dynamic measures 12,000K, Action measures 11,000K, Standard measures 9500K, Warm 1 measures 8000K and Warm2 measures 6500K... Warm 2 is "warm" only in comparison to the other modes. Since 6500K is nominally where you want to be for color temp (not a very good spec by the way, images can have way too much green or way too much magenta and still measure 6500K). Warm2 is completely unrelated to how you look for light bulbs, for example. In the light bulb world, 6500 is about as "cool" (they often say "daylight" because 6500 is pretty close to average daylight color temp) as home light bulbs ever get.