1997 Pontiac Grand Am fires up but shuts off after I let go of the key/ignition

I just want to first preface that this problem has only occurred on days where it's been VERY cold. I live in Illinois and it's been below 0 the past few days. I put the key in the key hole (which it's hard to turn because it's so cold out) and I turn the ignition to turn the car on. You can hear the car turn on but as soon as I let go of the key thingy, the dashboard lights up and all that shows up is the battery sign and "THEFT SYS". My battery is not even a year old so I know it's not that. I've also had it looked at multiple times by my mechanic and I know it's not the battery. Any tips? I've never had this issue and it only happens when it's super cold out. I've put HEET in my gas tank and the car started perfectly. I haven't tried that again yet but just wanted to see if anyone had any tips? Please!