On our Nexus 5X, enabling this option makes the screen way too cold/blue-ish - that's because the display was well calibrated by default. Thus, we'll just not going to let this toggle switched on. However, this option most likely helps if the display of your Nexus 5X has a yellow-ish tint - as you may remember, this yellow tint issue was present on some Nexus 5X devices since the very first batches hit the market back in October.
To turn the Cool color temperature toggle on, you first need to make sure that your Nexus 5X is updated to the latest Android 6.0.1 Marshmallow build - as mentioned above, the build is MHC19J (you can check that by going to Settings -> About phone). If the phone runs the latest build, you'll find the Cool color temperature toggle in Settings -> Developer options (by the way, here's how to enable Developer options on your Android device).
A similar Cool color temperature toggle is included in the Android N Developer Preview, which likely means that all devices running this upcoming version of the OS will have it (for the record, we don't know exactly when the final version of Android N will be released, but it should happen sometime this year).
Do you own a Google Nexus 5X? Have you discovered the Cool color temperature toggle? If yes, does turning it on make your display look better?