Car alarm/ heat, weather question?

I had a car alarm installed a couple of days ago. It worked fine no problem. Until I went to El Centro California close to Baja Mexicali where it was about 110 of heat. Well my alarm was acting up, I would activate my alarm and about a minute later the alarm would go on. So before I went to bed I activated the alarm again, no problem . I guess sometime in the night the alarm went on and I never turned it off and I think it killed my battery cause my car would not start in the morning. I also notice my car alarm remote battery was completely dead, I have one of those pager alarms. Ok my question is do you think the heat (weather) has anything to do with it? I'm back home here in Orange County California where the weather is a whole lot cooler and my alarm is working fine.