CPU Cores Overheating

[patonb]

You computers not bad.

Could you check what you Vcore is set at, both in the bios and by cpu-z.

 

[VCobra]

BIOS showed: 1.252 V
CPU-Z shows: around 0.850 V (but it occasionally varies up to around the same value as BIOS showed)

 

[patonb]

I think your default is setting your Vcore too high.

I'm pushing that Vcore on my 950 oc'd to 3.6Ghz.

I'd start dropping the vcore and testing with prime95 or LinX.

Lowering Vcore will lower your temps.

 

[Slaymate]

For Corsair A70 is a good cooler for the price, it's only $26.42 after a rebate at Newegg.
Newegg.com - CORSAIR CAFA70 120mm Dual-Fan CPU Cooler

I'm not really up on Gigabyte power supplies and if it is old I would replace it, but it is big enough for a 560 Ti. Even if you add a second 560 Ti later you won't need a 850w power supply, a 650w power supply (a good one) will run (2) 560 Ti in SLI though I would probably buy a 750w.
Newegg.com - CORSAIR CMPSU-750TX 750W ATX12V v2.2 SLI Certified CrossFire Ready 80 PLUS Certified Active PFC Compatible with Core i7 Power Supply

I would go with this EVGA 560 Ti with the Lifetime Warranty at $219.99 after a rebate.
Newegg.com - EVGA SuperClocked 01G-P3-1563-AR GeForce GTX 560 Ti (Fermi) 1GB 256-bit GDDR5 PCI Express 2.0 x16 HDCP Ready SLI Support Video Card

I don't really like the looks of the Phantom but if you like it that's all that matters, it doesn't come with all the fans, some are optional that you have to buy separately.

 

[VCobra]

@patonb: It was higher before I reset BIOS to defaults.

@Slaymate: Unfortunately, Newegg is off-limits for me. I live in Slovenia, where electronics are much more expensive. The A70, for example, is at least 50€ (which would be very cheap compared to the usual prices).
For the 4 computer upgrades/parts I listed earlier, it'd set me back at least 550€ (almost 800 USD).

And yes, the Phantom looks absolutely amazing to me.