BMW code P-code Fault type and function
227 P0188 Fuel trim (Bank 1), O2 control adaptation limit
228 P0189 Fuel trim (Bank 2), O2 control adaptation limit

How many miles on your BMW?
Have you replaced the O2 sensors?

If yes, is it possible you switched the bank 1 and Bank 2 connectors while changing them?

 

My 2001 330i has 142k miles on it. Never changed the 02 sensors since I've had the car at 69k miles. Don't know about previous owners. Isn't it very unlikely that they both would have failed at the same time, though?

 

All those codes are pending and not currently present.

 

That's what strange. It seems to be intermittent, because I keep clearing the codes and the service engine soon sign goes away for about a week, and then it comes back on.

 

exhaust temp codes are ghost codes. Our cars don’t have any exhaust temp sensors.

It’s almost certainly a vacuum leak, get it smoke tested

 

Clear them and see what comes back.

 

To fill in what the OP hasn't from his profile, the car appears to be a 2001 330.

OP said they have cleared them and they return.

Time to get in there and do some actual diag. Can you watch live data or data log with your scan tool? Fuel trim data will tell you a lot about what's going on with the mixture adaptation which the faults are for.

 

Oxygen sensors are wear items and should be replaced as they age and lose their functions. At the mileage you listed you should replace your pre-cat ones for starters as those have a bigger impact. Don’t skimp on the replacements, make sure it’s genuine BMW or Bosch direct fit.

 

Check the routing of the 4 O2 sensor leads to make sure that they have not dropped out of a clip and melted on the hot exhaust.

What are the 4 fuel trims and MAF value (g/s) at hot idle?

It's hard to get an E46 to run rich. It's usually a sensor soft failing (MAF or pre-cat O2's).

If you get stuck, set up OBD Fusion. Read the PDF in the thread on the settings. Run the 3 standard logs and a Rev-Rise log to check the MAF. Post links to the CSV files here and we'll have a look.

Rev Rise Test

This will check approx. the first 1/3 of your MAF's range.

Run your normal OBD Fusion log. Hot engine and Cat’s, stationary car. The test is best done just after a drive. Slowly raise the rev's of the engine (gradual increase) up from idle to around 3,000 rpm. I mean slowly. It should take you 3-4 minutes to do this test.

It takes some skill to do this test due to the lightly loaded engine. A little throttle change results in a large rev change. Don’t run up and down the rev range getting used to the control. If you stuff up the first part of the test getting used to controlling the small rev changes, then redo the test.