The following is my answer, the reasons for the heat and power running in the headphone jack of Apple 5s May be as follows:
Using the headphone for a long time leads to energy conversion at the jack, which generates heat.
The headphone jack chip needs power to work, which may cause heat in the jack.
Problems with internal components of the phone, such as faulty circuit boards.
To solve this problem, try the following:
Avoid using the headset for long periods of time, and allow rest time at the jack.
Replace better quality headphones to reduce the heat generated by energy conversion.
If the phone is still under warranty, you can contact Apple's official after-sales service for repair. It should be noted that if the mobile phone has a heating problem, you should immediately stop using the headset, and contact professional maintenance personnel as soon as possible for inspection and repair.