I fix xbox 360s as a side job. Please refrain from telling users to do the the "overheating fix." Letting the xbox 360 overheat does more damage to it.
The 2 red lights can be caused by various things:
1). CPU is overheating
2). GPU is overheating
3). RAM has cold solder joints under them, mostly the 2 RAM blocks left of the GPU.
I can't tell you how many customers have brought me their xbox 360 for repair after unsuccessfully doing the "overheating fix." I usually reflow the GPU with a professional rework station (the GPU is the culprit most of the time). Xbox 360s which have been overheated repeated usually require that I swap out the GPU, which requires a reball (expensive).
You can find out which issue the console is really having. When you see the 2 flashing red lights, hold the sync button on the console and press the eject button. This will give you some rapidly flashing red lights. Make note of how many quadrants are doing this. Repeat this 3 more times to obtain a 4 digit sequence.
Four rapidly flashing quadrants = a numerical 0
Three rapidly flashing quadrants = a numerical 3
Two rapidly flashing quadrants = a numerical 2
One rapidly flashing quadrant = a numerical 1
With the 2 flashing red lights, you will most likely get 0011 (CPU), 0012 (GPU), or 0013 (RAM).
If it's 0013, you'll most likely need a reflow on the two RAM blocks left of the GPU. The other two error codes might call for a reflow of the CPU or GPU also, but is probably due to the dried up OEM thermal paste.
If you have the 3 flashing red lights, you do the same sequence as above to get an error code sequence (most likely 0102, 0020, 0022, 0110, 0021, 0031, or 0103).
Once again, never, EVER do the overheating trick where you don't plug the fans in.