Disable alarm but keep keyless entry?

Is there a way to disable the alarm on my 2001 Blazer and yet keep the keyless entry active? For some reason when it gets cold at night (somewhere in the lower 50's and below), the alarm goes off and wakes everyone up. This is driving my wife nuts and her insanity is MY insanity! As it's getting colder now, any help would be greatly appreciated. I tried searching for something like this in the posts but couldn't fins anything about this type of situation. Has anyone ever seen this before? As it's getting colder outside now, any help would be appreciated.