2009 Chevy aveo starts fine; then stutters and dies in about 20 seconds

I've just put in a new thermostat and drove it to the gas station and filled it up. the next day in the morning i start it up (it's like 20 F outside) and it starts fine. idles up for like 20 seconds then while the idle comes down the motor is shaking and running like crap. I can hit the gas pretty hard to rev up the engine but it cant idle and eventual dies. then it starts right back up and does the same thing over an over. Help!

A few hours later i tried it again and its fine, what the heck man. oh and the temperature was like 5 f, maybe it just doesn't like it that cold. still any ideas whats up with this thing?

Any engine codes? Sounds like it could be the throttle body. I wouldn't run off and replace it right away though.