It might be piston slap my 06 cobalt ss with the 2.4 had it real bad. It did it from new to 9000 miles before I traded it on my 07 2lt. They did something to the 07 2.4 to stop this noise I think it was new liners for the cylinder walls but im not sure but my o7 2.4 in my 2lt dont make any noise on start up.

 

pea420 sorry about post newbie. sounds more like tapping
makes tapping sound while acclecrating .
gone when engine reaches operating temp.