I have a 1998 SL2 Saturn with the stock OEM alarm system. Now this alarm is very weird. When it gets cold outside it will quit working. By quit working I mean the remote will no longer unlock or lock the car. I can hold down the lock and unlock buttons for 10 seconds next to the car and the car will honk and lock/unlock the doors and it will work for a bit then stop. When it is warm outside (60F+) it works no problems.

Things I have tried:
- Replace batteries in original remote
- New remote (programmed it to the car)

What else could I check to see what could cause it to not work in the cold? Is there a fuse that I can check? Where is the module that control the system and is it replaceable? How much does it cost to get a new module?

Any information is appreciated.