Hmm, from the z820 datasheet i've seen a z820 doesn't support an E5-2960. As such i'd assume that possibly it's a simple typo on your part and maybe you actually meant that you have an E5-2690. If so, dyslexics of the world untie 
Anyway, i'd Initially take a different tack as presumably any z820sold with 2x E5-2690's should work as intended and spend at least a little time in turbo boost speed of 3.8Ghz before throttling. So if it's under warranty, i'd get HP to look at it, otherwise possibly applying new and better thermal paste could help.
But if you upgraded the CPU's yourself, you may want to consider that HP workstations sold with power hungry CPU's utilize a high power heatsink/fan combo or indeed water cooling. From memory, a high power heatsink/fan combo looks like the normal assembly though it has an extra jumper wire on the connector side you plug into the mobo and it is a slightly larger heatsink with more cooling pipes. In any case, if you used a high power CPU with a normal heatsink/fan assembly, i think you get a BIOS warning during boot but not sure. Such normal & high power heatsink assembly discussions can be fount on these forums or others forum guru's may be better able to elaborate on such issues than myself.
If water cooling floats your boat, HP has already solved such issues and you can read about it here
Other than that, i can't help heuther since i don't have a z820.
[edited to add]
Maybe i'm remembering z800 heatsink/fan assemblies but searching these forums may resolve this 
As another hint, clearing CMOS has sometimes helped in some fan speed issues so always worth a try (but do take not of any non default settings youve made).
