This morning I experienced something similar, but not quite the same. I'm thinking it might be related, but don't know for sure.
It was 49/50-ish this morning when I started up mine to head to work. It fired right up and ran fine until I came to the first red light. The engine shut off, and the Auto Stop/Start lamp was illuminated on the dash. A little freaked out, I hit the Auto Stop/Start Off button, and the truck fired right up, and I went on my way when the light turned green. It never happened again, and ran fine later the in afternoon after it had warmed up a bit and I went out for some lunch.
I know this sounds pretty normal to those with Auto Stop/Start... however, when I bought my truck, the previous owner had disabled the function, and not being a fan of it myself, I happily left it disabled. So basically, this was the first cold morning I've owned the truck, and the first time it has done this (turned the Auto Start/Stop on itself). I believe I had a similar issue a few weeks ago, but I didn't pay as close attention to the dash lamp (didn't notice it, but experienced the same 'feeling' when the engine shut off and started back up at a stop light). I'll definitely be keeping an eye on it.