iPhone 4, repeating tone won't turn off

[309green]

Twice in the last hour (once when making a call and once after missing one) my iPhone 4 began to repeat a noise and didn't stop until I played music or shut it off.

No the sound is not an alarm. It sounds like the very beginning of a phone call that stops abruptly and repeats.

Earlier in the week my phone overheated, could that have anything to do with it?

 

[EricNau]

I'm assuming you've since tried restarting the phone? If so, then the next step would be a Restore in iTunes, first from backup, but fi the issue persists a Restore as new may be necessary.

iTunes: Backing up, updating, and restoring your iPhone, iPad, or iPod touch software

Also, have you contact Apple Care? It may be good to have your issues documented, in case you need to get repair covered under warranty at some time in the future.