When your Pixel overheats, it currently displays a "Phone is getting warm" alert. Google is developing more detailed alerts that provide additional information without requiring the user to visit an online help page.

The notification that is now in place describes how "some features are limited while phone cools down."

Google describes how to "Tap for more info" as follows: "Your phone will automatically try to cool down." Your phone could operate more slowly, but it can still be used. Your phone will function normally after it has cooled down. 

Device Health Services version 1.27.0.638152889 shows that additional detailed alerts are being worked on. 

The "pre_emergency_notification" with the title "Phone needs to cool down:" is displayed first. You might notice a decrease in performance. Try staying out of the sun and shut down any battery-hungry apps.

"pre_emergency_dialog" in its entirety