Battery draining quickly

I bought a new iPhone 13 and it’s been 2 days. I think the battery is draining too fast. Even today I had to charge my phone 2 times. The first charge I did till about 70 percent. Came back home after 2 hours. In that time I used the phone around 15 min. Had about 62 oru 58 something battery left. Turned on the device hotspot connected my tv at 60 percent or something went to sleep at 3.30 pm and woke up at 9.20pm and the phone was at 19 percent battery. I think that’s a lot off battery for a phone that’s sitting at idle. I called the tech support at day 1 and they told me it’s because the phone is new after a few cycles the battery will be optimised. Also while charging the device is heating up at the back and sides. Guys any suggestions (Apple what is this)