That's strange.
The point of cooling mod is that HMG starts shooting a little bit faster. Well not actually faster itself, it shoots 3 bullets as normal but the recoil time is a little bit smaller. After some active using the cooling system stops working (worn-out maybe) and HMG looks and shoots as usual one.

I read in a pc magazine that the cooling mod reduces the clip size so that you can shoot the gun single shot instead of boom-boom-boom wait boom-boom-boom

Maybe they made a mistake.
At youtube you can find videos of kingpin's gameplay that shows this.
Like this http://www.youtube.com/watch?v=1y_RFZTDzH0&feature=related - at 27 second HMG with cooling mod still shoots boom-boom-boom-wait-boom-boom-boom