MacBook Pro 2011 15" when it is very cold weird graphics problem

Bart this sounds like a GPU issue (20-30 second - everything is PERFECTLY working and NEVER EVER comes back” perfect timing for a processor to reach its working temperature)  What you have is that the metal constricts in the cold and thus does not make contacts. Once it warms up it will once again make contact. This could be cold solder joints but it could also be an issue with the solder bumps. Here is a quick and dirty explanation of why this could be happening.

It is not always a failure of the solder balls which connect the Flip Chip BGA package to the motherboard. It does happen and you can see why [ http://www.bunniestudios.com/blog/?p=223|on here] More commonly however is that the failure is due to the chip design itself.

As you can see the "bumps' are what actually connects the die to the substrate to make the chip complete. If these bumps fail the die does no longer make contact either he substrate and thus no contact with the circuit board. The chip has failed.

Here you can see the space where the bump has failed and no longer makes contact. We are talking microns of space here. So a bit of pressure on the top of the die potentially close the gap. Same with a reflow, it may allow some of material from the bump to reshape and starting to make contact again. The heating of cooling of the chip during use is what will eventually cause it to fail again.

Now in theory you could prove that all you would have to use is some freeze spray and apply that on the GPU while it is processing. If the same anomalies show up you know the cause is your GPU. You may not do this if you fear that the rapid cooling could actually crack the IC.

The other thing you can do is to attach an external monitor. If that acts identical you know it is not your LCD.