BMW 318 Forum : “warning beeper”

This might be related to your memo button on your OBC (on board computer). When you set a time on the memo it will sound with a beep to remind you what time it is. That could be your problem with the sound.

If the temp gets below a certain point outside, there is a warning beep... Not sure if thats it, but it is a possibility.

I have a 1992 318is and I hear a single loud beep occasionally.  It sounds at random times. I know this because I wrote down the time
and settings of my dash board every time I heard it. Does it have to do with the check engine or oil maybe?

My car beeps once when the outside temp is at or below 37 degrees.  It does that to warn the driver of potentially slippery roadways.

Check the time at the moment of the beep.  Generally (by experience on the 92 535i I had) it sounds from 30 to 15
seconds before the next hour.  If you have the outside temperature sensor missing it might always display 37F and thus
warn you with the beep of the icy road conditions, regardless of the real temperature.

You might want to check for that behind your bumper cover.  These things come loose most of the time with age.