I have been getting BCC 124 blue screens in both Win 7 and Win 8 (separate OS SSD's for each OS) and WHEA errors which point to the CPU (mostly core 2 but occasionally core 3).
 
I have run memtest86 and no errors, the Intel CPU diagnostics and all the CPU tests on the UBCD (Ultimate Boot CD) and nothing shows up. 
 
I have swapped memory (from GSkill to Corsair), no change.  Replaced the motherboard (with a spare on hand), no change.  tried a different power supply, no change.  Used the Intel HD4000 graphics, no change, used a Radeon HD7700 video card, no change.  Disconnected all the SSD/hard drives except the OS drive and it happens in both Win 7 and Win 8, so no change.
 
The only thing left is the CPU. The CPU cores idle around 30C and rarely go over 40C so heat is not a problem. 

It's possible that the CPU is defective...
But (FWIW), out of thousands of machines the past 20 years, I've only experienced a handful of bad CPUs.
It's very rare...

What else is left?  It happens on Win 7 with only the Win 7 OS SSD, an Intel, connected.  It happens with Win 8 with only the Win 8 SSD, an OCZ Vertex 4, connected. 
 
Everything else has been changed - One item at a time.
The memory from GSkill Ripsaws to Corsair Vengeance (both DDR3 1600 and listed as compatible on both motherboard memory lists).
The motherboard from a Gigabyte Z77X UD5H to an ASRock Z77 Professional.
The Power supply, from an Antec 650 watt modular to a Corsair 750 watt modular.
With a PCIeX16 video card, or without using the Intel HD4000 graphics in the CPU.
Disconnected the internal optical drives.
 
As a side benefit, I gained extra USB ports on the ASRock motherboard, enough that I don't have to use a PCIe USB port card for the needed USB ports.
 
 
 

New CPU installed (same as original an i7 3770).  No more WHEA errors or BCC 124 BSOD's. !!!!
 
 

fireberd
New CPU installed (same as original an i7 3770).  No more WHEA errors or BCC 124 BSOD's. !!!!
 
 

Glad you resolved it fireberd (if anybody could, you would!!)......with all the things eliminated, that would've driven me nuts not knowing what caused the BSOD. Very unusual to see an i7 fail like that.

I just got an RMA from Intel.  Looks like they will replace it under warranty.  I'll install the replacement in my backup system, and give it an upgrade.
 
Unfortunately I had to buy the new CPU.  Everything else I had on hand.