iPhone SE (3rd Gen) Battery Issue

What's the battery's maximum capacity percentage in Settings>Battery>Battery Health & Charging ?

Reading your question, it sounds like that battery is faulty, but we, just user like you, cannot diagnose that issue remotely, sorry.

I suggest that you make an appointment (*) and have your device inspected at an Apple Store or AASP (Apple Authorized Service Provider) among this list:--> https://locate.apple.com/choose-country-region . After checking it out, they'll give you all the available options.

Regards

Giulio

(*) You can do it:

• Online:--> Genius Bar Reservation and Apple Support Options - Apple;
• Contacting a local Apple Store or AASP among the list provided above;
• Using the "Apple Store" app, available and downloadable from AppStore.

Well, it seems a good percentage, but reading the symptoms you provided (unless you're using your iPhone beyond suggested temperatures, as per this support article:--> If your iPhone or iPad gets too hot or too cold ) make me think of a battery problem.

Please keep me informed.

Thanks and regards

Giulio