Upgrading my CPU and do I need new CPU cooler?

I am replacing my CPU with this one AMD Phenom X4 Quad CPU 9500 AM2+ 2.2 GHz 3600MHz 4MB but this one comes with no CPU cooler and heatsink I am wondering if the one I have now for my dual core AMD Athlon will work this is the model on the one I have now AMD 64 X2 CPU Fan and Copper Pipe Heatsink 2ZR71-409. Am I going to have to replace this also or will this one work. I could get the Cooler Master 200Watt V6 CPU cooler but only if this one is not strong enough. Thanks for your help.

I just bought some new paste from the computer store and I don't over clock any of my CPU's. I think it's a good idea to clean this cooler and heat sink first what would you say would be good to clean off the old paste and dust?

I was told by the computer shop to use warm soapy water and a clean soft rag and dry it off really good. Well that's what I always did anyway. I have been building/working on computers since 2006.

Oh sorry about that I was only posting the last reply saying what the computer shop said to me I didn't think I would get a reply. Thanks for telling me that the CPU cooler I have now will work this saves me some money. It seems that the shops around here don't know what they are talking about they also told me the cooler I have now won't be strong enough where it's for daul core not quad core rated.

The only thing I am worried is this cooler is about 5 years old already I think this is why the shop told me to replace it. They said the fan is only designed for so many hours of use. It does look like it works fine but do they have a point?