My car remote is malfunctioning?

I have a 2008 Hyundai Accent. It seems kind of weird but recently I have noticed that the remote to unlock the car doesn't want to work when it's really hot out.. this could just be coincidence, really.. but that's what it seems like to me. Always works in the morning and at night, but never during the day when it's scorching. Anyway. Yesterday the remote wouldn't unlock the car when I was leaving from work so I unlocked the door with the key. Then when I tried to turn the car off, the panic alarm went off when I turned it on. Not thinking, I turned the car off first and then turned the panic off (it turned off after I pushed the button about five times!). Then I turned the car on again and the same thing happened. This time I turned the car off just to see if it would do it again. A third time and the panic alarm went off when I turned the car on. Of course I kept the car on and turned the panic off that time. When I got home I turned the car off and back on just to test it and it turned on without it but the remote didn't lock the car. This morning when leaving for work the remote unlocked the car and the car turned on without the panic alarm. I am aware that the battery is probably dying in the remote but my real question is this: If I take the remote off of my key ring and leave it at home, will the panic alarm still go off sometimes when I am turning on the car? I don't want to be out somewhere with the panic alarm going off and no way to turn it off. I figured since it seems to be the remote battery causing the issue that if I leave the remote as far away from the car as possible, this won't be a problem. Am I right?