Upgrade beyond Dell Optiplex 360's support configuration

Specs for the Optiplex 360 desktop are in this doc

 It lists compatibility with a Core 2 Duo, but does not list Core 2 Quad.

This system only has 2 RAM slots and the doc says the max RAM is 4 GB (eg, 2 GB in each slot).

Unless somebody knows differently, I don't think what you're proposing is going to work.

The Intel G31 chipset is limited to 4GB, so 8GB is out of the question:
http://ark.intel.com/products/chipsets/30686

Like Ron's doc, this one does not include any quad-core processors either:
http://www.dell.com/downloads/emea/products/optix/Optiplex_brochure_360_en_new.pdf

However, referring to the Intel specs on the G31, there are only two quad-core processors listed as compatible with the G31:  Q6600 and Q6700, so if you wanted to try, those are the only two that would have a chance of working. 

Besides chipset support, BIOS support is usually required for a given processor to work, so make sure to update your BIOS before attempting it.  None of the BIOS updates for the 360 mention anything about adding CPU support to existing code, so don't be surprised if it doesn't work :)

Well, at least 4GB of ram is good enough, Im willing to try Q6600 or Q6700 quad core processor. Wish me luck lol

Good luck!  Please let us know how it goes, so we have a more definitive answer for the next person to ask :)

I'd like to know how this guy got on,

I got the same computer and wanted the same thing.

mine is an Optiplex 360 tower with Intel core duo 2.8,

I noticed in a link above to instruction manual for this computer there was some other more powerful Intel chips listed than mine, all were core duo. So would any of these fit on my motherboard and simply work?

This is a belated reply, but I did just this, only not that much RAM.  Just 2 gigs.  The Core 2 Quad works great by being responsive and snappy compared to the Celeron 350 single core that had originally been there, BUT the computer was designed with a large fanless heatsink, and it's not adequate to keep this CPU cool.  Two 120mm fans can do the job, though in a push pull arrangement.  I installed a CPU temp monitor to keep watch.  Just one thing I don't know is whether the chipset on the mobo can handle the raw power this CPU can draw without a lot of heat, so my next mod will be an extra fan for the mobo.

I know this is old but I had to chime in when I read the OP. I have a Core 2 Quad Q6700 working fine in my Optiplex  360 with A07 BIOS.  Your stock heatsink and fan will not cool this processor being that it pulls 95 watts. You will need an aftermarket HSF. I'm using a Rosewill RCX-Z300 92mm Ball CPU Cooler with Arctic Silver 5 Thermal Paste.

Reagrds!

Sweet! Good to know! The price for these old procs makes them well worth while. Breaths new life into these machines. I'm using mine with a 2GB GT 730, an LG Blu-ray drive and a Logitech K400 for a home theater. works great!  What  I haven't tried yet and would love to know if I can do more than 4GB of RAM.

Cheers!

The total amount of available memory will be less than 4GB. The amount less depends on the actual system configuration. To fully utilize 4GB or more of memory requires a 64-bit enabled processor and 64-bit operating system

Several models have chipset limitation and Video RAM shared that you never get back.

In those cases you never ever get the max you get 3.2 to 3.5 gigs period.