Windows phone 8.1 good and bad

About a month and a half ago I got a Nokia Lumia 1520. I love it. I registered as a "developer" on appstudio, and got windows phone 8.1 as soon as it was available. I love it. There is one big problem though: battery life. The 1520 has quite a large battery, and used to be able to last me up to two days. Since I got 8.1 though, the battery life has been terrible. In standby mode, it will drain to battery saver mode in about 5-6 hours. The recent update to 8.1 helped for a few days, but recently the battery life issues started back up again. This also makes the phone almost unbearably hot against my leg while in my pocket. Most of my apps are not allowed to run in the background. I also like Cortana, so I leave location services on.

What could be happening with 8.1, and is there any easy solution to it other than disabling notifications, and Cortana?