iPhone 5s constantly overheating

Have any parts of the phone been replaced recently?

Did you use the backup after setting it back to factory settings? If yes, try again, this time without the backup data, to make sure that it does not contain corrupt data, causing this issue.

You can also visit an Apple Authorized Service Provider next to your place to get the phone checked.

Find an Apple Authorized Service Provider

If Apple opened the phone to check it and the heating problem occurred after that, bring it back to them, repairs done by Apple are also covered by a short warranty period.

As far as I know, repairs done by Apple are covered by a warranty of 90 days, you can also choose to go to an Apple Authorized Service Provider or another Apple Store, your service history should be in the system.

3. Warranty and Limitation of Liability

3.1 Service Warranty. For all service orders, Apple warrants that (1) services performed will conform to their description for ninety (90) days from the date of service, (2) except for batteries described in the subsection below, all parts or products used in service will be free from defects in materials and workmanship for ninety (90) days from the date of service, and (3) batteries installed as part of Apple’s battery replacement service for Apple portable Mac computers will be free from defects in materials and workmanship for one year from the date of service. This warranty is an express limited warranty. If non-conforming service is provided or a defect arises in a replacement part or product during the applicable warranty period, Apple will at its option, either (a) re-perform services to conform to their description (b) repair or replace the part or product, using parts or products that are new or equivalent to new in performance and reliability, or (c) refund the sums paid to Apple for service.

copied from: Repair Terms and Conditions - English

Start a service request

Find an Apple Authorized Service Provider

Make an Apple Store appointment

You're welcome 🙂