Another addition: Box coolers are completely sufficient if you do not overclock. And since this is a non-K CPU, i.e. not overclockable, the issue is settled. Never buy extra coolers if you don't want to overclock. At most if you absolutely want a quiet PC, or if you want something aesthetically more elaborate.
Yes, a cooler is included here, but it is relatively weak... Google for "Boxed Intel Cooler".
Whenever you see BOX or BOXED on Intel processors, you know that an air cooler is included.
the difference between boxed and unboxed is that the unboxed ones were already used... These were sent back to Intel by customers because they usually have a bug or a weakness/defect... so always go for BOX processors :)