Will it work?

[Yo-Yo]

How much of a cooling device would I need for a Celoron D 2.8 GHz Processor?

 

[TheChef]

Depends on if you are going to overclock or not and if you will be using processor intensive programs. Tell us what you plan on doing with it.

 

[NeuromancerWGDD'U]

I'd imagine that as long as you're not planning on overclocking it at all (or if you plan on overclocking by a very small amount) the stock cooling would be fine.