Apply thermal on cpu?

[Xanikac]

So heres my question.

Im about to upgrade my intel core i3 2100 to intel core i5 3570k,and also buy a Corsair Hydro Series H60 witch has already thermal paste on it.
People when they install a new cpu put thermal paste on it right?
Do i have to put thermal paste on my new cpu, then install the H60 witch has already thermal paste on?
And does the cpu comes with its own thermal paste in?

Might sound stupid,

 

[Platinum Era]

The H60 comes with paste pre-installed so all you have to do install the 3570k and then install the cooler.
The stock coolers and closed loop water coolers come with paste pre-installed while after market air coolers come with paste you have to apply yourself.

 

[Xanikac]

The H60 comes with paste pre-installed so all you have to do install the 3570k and then install the cooler.
The stock coolers and closed loop water coolers come with paste pre-installed while after market air coolers come with paste you have to apply yourself.

Ohh...right thank you.