Why is an incandescent bulb hot to touch when it has been switched on for a while?

Answer 1

http://www.highlightskids.com/science-questions/how-do-light-bulbs-work

Answer 2

The incandescent bulb heats the filament (typically a coil of wire) to thousands of degrees so that it glows.

Since the bulb itself is generally at most a few inches from the filament, it gets pretty hot as well.