Can you properly test for overheating on the ground?

More food for thought,

Along with air flow check things like coolant and oil hoses that are partially collapsed from too tight a bend to poor routing. Basically a reduced hose I.D. radius. A coolant or oil thermostat malfunctioning. Too small a hose I.D. Someone tampered with the internal carb setup. Airflow through your air filter. If it is being restricted at all it can be a cause or contributing factor.

Plus it may not be any one thing, but a couple of things contributing to your issue. Take the time and rule in or out each item. Don't throw money and parts at it. Do these simple easy and simple checks first. Look toward the most common causes first.

Thanks, Sean and Roger.

I've got a Rotax mechanic helping diagnose it but we are both scratching our heads.

Idle is rough, and seems to be missing slightly at low RPM. 

The overheating came after The carbs were rebuilt, new fuel lines, radiator flushed, new muffler. 

We found 2 small things that didn't fix the problem, exhaust valve not sealing properly (fixed), and an intake gasket that we thought was causing an air leak (it wasn't).

A few people have mentioned airflow over the radiator is critical. Would the radiator get proper airflow on a ground run? We have not test flown it since the head was removed for valve work. 

Is it oil temperature?

OR

Coolant temperature?

If Both which one goes up first?

If the carbs were just done and that's when it all started I'd be pulling the carbs back apart.

It should not need inflight airflow to prevent overheating.  A 912 should never overheat  on the ground.  Rotax recommends idling on the ground to cool the engine down if you’ve been running it hard right before shutdown.  Did you confirm the temperature indicating systems are operating correctly? Sending units good? Grounds clean and tight? After the carb rebuild did you do a full carb mechanical setup and pneumatic synch?