Florian,
1. Definately clean out the combustion chamber, but be aware that the
gasket is no longer available from Dometic, so exercise care in separating
the two halves of the combustion chamber.  Since I found the gasket lacking
in resiliency, and its ability to seal quesionable, I used a very thin film
of gasket sealer on re-assembly.
2. Confirm that the drain tube is free of obstruction.
3. Check the thermo switch that is mounted on the upper cooling fins, for
reasonably good contact with the fin; sometimes the retaining ring becomes
loose.  Some thermo-conducting paste can be added between the fin and the
switch, but that's optional.
4. With the fridge powered temporarily with 12 volts, the operation of the
thermo switch can be checked by applying heat with a heat gun or hair
dryer; obviously this allows checking the operation of the fan also. I'm of
the opinion that if the original fan is working as it should, that's all
that's needed.  Design Note: the thermo switch is supplied with 12 volts
whether the fridge is turned on or not, so the switch, and thus the fan,
will be activated by high enough ambient temperatures.
5. Blow out the intake and exhaust tubes.
6. Though I can't say for certain, I seem to remember that when installing
the check valve update kit, the directions to enlarge the inlet and outlet
(Bentley 76.26) contained an error with respect to the size of drill bit to
use, too large a bit for the job I think.

Unrelated to the fridge proper:
A. If you use the city water supply, check the plastic elbow for cracks.