Battery problem

Your iPad will automatically limit charging to ~80% is some circumstances to protect the battery - this often occurring when the ambient or device temperature is relatively high. If your iPad is within a fitted case, this can negatively impact natural cooling; removing the iPad from its case (where used) may help with cooling.

Do you leave your iPad connected to its Power Adapter for extended periods? If so, this is not of itself an issue - as the iPad will optimally manage battery charging. When connected to a Power Adapter for an extended period of time, such as when used in Kiosk or PoS (Point if Sale) applications, iPad will change its charge management strategy - and reduce the maximum battery charge level to about 80% of maximum capacity. 

This strategy is intended to extend the life of the battery by reducing chemical ageing that occurs when the battery is continuously maintained 100% charge. As soon as a “normal” charge/discharge pattern is resumed, charge to full capacity is restored. If your iPad has paused charging at ~80%, simply disconnecting the Power Adapter from the iPad for several seconds may trigger completion of the charge. 

Ambient temperature is also a contributory factor in charging being paused; the iPad is designed to reduce the charging rate if the temperature is too high for optimal charging. Summer high temperatures may cause this protective measure to be triggered. Try moving yout iPad to a cooler location whilst charging.

More information about iPad’s battery management can be found here:

About iPad and iPhone Charge Management Feature – Apple Support

Otherwise, if a fault is suspected, a visit to the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP) is recommended. Here the technicians will be able to test and assess your iPad - and you can explore your available options:

Genius Bar Reservation and Apple Support Options - Apple

It shouldn't get that hot just charging unless it's in a really hot place. I've only seen a temperature warning when I was using it outdoors in bright sunlight trying to stream video using public Wi-Fi. It was the sunlight making it really hot where it gave a cool down warning just to use it.

I will say that being in that condition didn't preclude Apple from providing a warranty replacement when the charging/data connection failed. I don't know if it was recorded in the diagnostics somewhere.

No, this is not normal and yes, you should schedule an appointment at your Apple Store Genius Bar for evaluation and options.