Why is my iPhone 13 showing a temperature warning after getting wet?

Apparently, your definition of "works perfectly fine" is different from most people's...

As already stated, liquid damage is not repairable.

The device is now a fire/explosion hazard as liquid/corrosion can reach the battery and charging circuits.

Shut it off, put it in a fire safe container, and make an appointment at the Genius Bar of your local Apple Store.

You may be eligible for a discounted out of warranty replacement.

Continuing to use an iPhone displaying a warning is a safety hazard. The iPhone should be powered off and placed away from combustible materials.

Your device contains lithium ion batteries. Lithium does not like exposure to water/moisture. Don’t take my word for it. Google it.

Contact Apple Support.

If you’re in the US please call  1-800-MY-APPLE or outside the US, consult the support articles below.

Contact Apple for support and service - Apple Support

Genius Bar Reservation and Apple Support Options - Apple

Explore Service Locations

Official Apple Support

Live Chat with an Apple Advisor in Messages. 

Anna_SB wrote:

The iPhone still works perfectly fine though. It is charging, powering off and connecting to wifi

If the phone is showing a thermometer on it, it's not working just fine. Water damage can manifest in many ways. Apple won't attempt a repair on a phone which shows it has been wet and the sensors will demonstrate that. You can certainly take the phone to the Genius Bar at your closest Apple Store, but you should NOT be surprised or disappointed when they tell you the phone has to be replaced due to liquid detection.

Because the sensors have been damaged by liquid exposure.

It's effectively toast.

Liquid damage is not repairable. The phone will have to be replaced.