Ummmm... I would have taken it back to the store and asked for a replacement.
That is not normal at all. even with the device's settings left alone, there should not be any issues with responses with touch.
Note... The pen feature is totally separate from touch. The screen has two different features, one being a digitizer for the pen function the other for touch. It is possible that during assembly that the connection for the touch screen is faulty, as a bad solder joint during wave process could make the connection heat related. As the device cools, the contacts contract causing a fault with touch operation. When heated up from normal use, expansion forces contact between connector and board for normal operation to function with touchscreen.