2012 GLK350 has the shakes
If you've been running with a bad T-stat, you would've been running rich since most likely the T-stat failed in Open position, meaning your GLK never really got up to temp; but it was injecting more fuel trying to warm it up. You may want to try a good fuel injector cleaner perhaps? When was the last engine air filter change?
You mentioned you've cleaned the MAF and MAP sensors, that was probably a good idea. How many miles? Are you on the original oxygen sensors? Any EVAP issues? I would invest in a decent scan tool so you can monitor fuel trims and individual injector quantities, you may be able to better diagnose the issue.
The O2 sensor(s) (there are two, one pre-cat and one post-cat) can be operating within spec, just dirtied up and slower in providing data to the ECU by being in the exhaust stream for 93K miles and 9 years. If they fail, you'll get codes for sure. I would maybe check for any vacuum issues as well as the PCV system. A dirty/clogged PCV valve would affect the way it runs.
Modern MBs have sensors and computers in all sorts of places because they're overengineered. Oftentimes it's not a physical fault with a part, it's a sensor that goes wonky for no reason. It's just part and parcel of owing aging German vehicles. Again, a good scan tool would reveal things we can only guess at. They're worth owning if you plan to keep a German car for the long haul.
I would try a few tanks for fuel injector cleaner and perhaps an "italian tune-up" as often as possible. Hopefully others can chime in.






