If the phone is using GPS, then yes, turning it off will help. I'd think you'd see the GPS indication in the status bar if that were happening. I suspect it's something else.
You could go into Settings | App Manager, scroll all the way to the right till you see "All", then scroll down till you see System and you could clear the cache, and power cycle the phone.
You might also be in a fringe area and your phone is changing modes to communicate with the towers...
You are on T-Mobile, right?... Did you get the KitKat update already? You can determine this: Go to Settings | About Phone |Software information, and if you are on 4.4.something it's KitKat.
If so, I'd recommend backing up any music or images or other content you don't want to lose, copy down email settings and the like, then I'd perform a Factory Data Reset (FDR).
Many many times, an Over The Air (OTA) update to the OS seems like it's working fine, when it isn't - and you see bizarre behavior, sometimes battery consumption as a result.
I've even read about people saying their phone, out of the box, consumed battery resourced rapidly before they "reset" it.
I know that performing a reset is likely to cause you some effort to set up your phone back up again (specially email). But that's what I'd recommend.
Report back.