I'm confused.

I bought a thermostat from Autozone to replace the one that I have because it was all broken up and besides..I'm replacing the radiator today. Anyway...I want to be sure I'm putting it in right because the car ran hot after I had finished the radiator replacement (of course filled with flush + water). Which way does the thermostat go in? Does the thermostat have to have one of those little jiggly things? (this one doesn't). Does the spring part go down towards the engine? Someone told me that there's only one way that the thermostat will go in; however, the one I have from Autozone will go into the little housing both ways (of course with the o-ring). Help this confused man.