As a GTX 1060 (6GB SC) owner I feel sorry for you OP.
I've had EVGA 750 SC, 960 SC and now 1060 SC, and have opened them all before. EVGA has never actively cooled the VRAM/VRMs, and the 960 SC and 1060 SC pretty much have the same cooler.
Now my question is, is what happened to OP truly isolated (these things can happen, and doesn't necessarily indicate a fault), or is it indicative of an issue with the VRAM/VRM temps? Did EVGA used lower quality VRMs compared to the 960 SC? Is the VRAM an issue due to it being clocked 1000MHz higher than the 960 SC, hence generating extra heat in that region?
This is the GTX 960 SC. There are no thermal pads whatsoever. I didn't take a photo of the 1060 SC when I took it apart, but the cooling solution and heatsink is basically the same.
http://i.imgur.com/sR4IvQs.jpg Hopefully EVGA can assuage our fears here. If there are more widespread reports I will definitely try to send this back to Amazon.
It also wouldn't hurt for EVGA to extend the thermal pads to us owners of the GTX 1060 as well. Good lord I hope EVGA doesn't cheap out on those in the future. They cost at most a dollar per card.