Constant Speed Propeller

You run the engine at full power and RPM (~5800) in the initial climb at speeds that are likely below what you normally cruise at and have no cooling problems.
This indicates it is not a cooling issue.
It is a loading issue.
At cruise, you pitch for the low 5000rpms but there is No mention of Manifold Air Pressures (MAP).

In the Lycoming/Continental world, the unofficial rule is to not "Go Over Square" with the MAP.
We can apply that same rule to our 912 engines with a simple correction factor.
A working rule of thumb for the Non-turbo 912 engines is to keep the MAP less than the RPM in hundreds divided by 2.
i.e.
5400rpm = <27"Hg MAP
5200rpm = <26"Hg MAP
5000rpm = <25"Hg MAP

The engine will thank you for it.

Yes Bill - this is the same conclusion I have taken so long to come too. 

The Airmaster CS prop has factory settings for Take-OFF (TO), Climb & Cruise - there is a manual override which allows the pilot to Fine/Course the factory settings. Further, the factory settings are all 50 RPM below Rotax published Max rpm eg TO 5750 rpm, Climb 5450 rpm, Cruise 5450 rpm (I have only ever seen 5350 rpm)

Some more detail:

CS Cruise, Alt 3500ft, OAT15C, Indicated Air Speed 133Kn, RPM 5160, MAP 26.1 

CS Cruise Alt 4500ft, OAT14C, Indicated Air Speed 132Kn, RPM 5400, MAP 24.7, Oil temp 115C

CS Cruise Alt 2600ft, OAT 17C, Indicated Air Speed 125Kn, RPM 4760(?), MAP 27.8, Oil temp 106C

CS Cruise Alt 4000ft, OAT 12C, Indicated Air Speed 136Kn, RPM 5200, MAP 24.8, Oil temp 109C

CS Climb, Alt 3000ft  OAT 11C, Indicated Air Speed 105Kn, RPM 5230, MAP 20.7 Oil temp 104C

Next visit to airfield, will measure Oil Cooler to make sure of size.

It sounds like you have some experience with this problem. Although our installation is similar, there is a major difference. My cooling airflow goes through the radiator first and the through the oil cooler. They are mounted in tandem and lapping each other about 1 1/2” with a silicone seal baffle. In the plenum inlet opening is a splitter that directs 90% of the airflow to the radiator. I’ve never had problems with oil temperature and this setup gives adequate cooling for the radiator which I had trouble with. Just a thought.

If Cruise is electrically programmed to 5450 rpm, you should see 5450 rpm Plus or minus a little bit. (The reason for the 50 rpm servo dead-zone buffer.)
Have you confirmed the COARSE and FINE Soft Mechanical limits?

The COARSE/FINE Soft Mechanical limits are to prevent a Propeller Runaway if the controller were to fail.
These keep the prop within a reasonable pitch band that would at least allow continued flight.
The setting of these limits is unique to each aircraft.
They are NOT set by the Factory.
See your Owners Manual. Chapter 8, Page 61.

The FINE limit should allow the prop to reach its Full selected Static RPM (5750 rpm) at Take-Off Power just before brake release.
The Coarse limit should allow at least a minimal Climb at Full Power with the engine lugging badly. (~4500-5000 rpm ???)

As you reduce the throttle, the Cruise RPM should remain at 5450rpm until the FINE Mechanical limit is reached at some lower power setting.
Do you see the COARSE/FINE Limit lights in flight other than when reducing power in descents?

 Hi Sam,

Any chance of some photos of your engine/cooling instillation?