Not normal. Take it to an Apple Store for evaluation.
Make a Genius Bar Reservation
http://www.apple.com/retail/geniusbar/
Try this - Reset the iPad by holding down on the Sleep and Home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider - let go of the buttons. (This is equivalent to rebooting your computer.)
Or just turn cellular off like you have been doing.
Cheers, Tom