Good morning Balázs.
Oil should cover the lowest, rippled section of the Jabiru dipstick.
As the others have said, your airspeed is important; when I climb out steeply, at 60knots, the heads heat up fast, because they’re getting much less airflow.
Jabiru is one of the most intensively-tested aircraft, but I bet the factory only tested their engines installed in Jabiru airframes, which are not designed for slow flight. Therefore, avoid low airspeeds while at full power.
Your oil cooler looks like mine, which has been very successful for years. The difference is that mine is mounted horizontally, under the spinner, so it gets plenty of airflow. If yours has been squeezed inside the cowling at an angle, it may not be getting good airflow, unless you carefully design and seal the ducting.
You are right to be concerned about overheating the cylinder heads; the alloy Jabiru used is suitable for CNC machining, but not as heat-tolerant as some other engines. If overheated, it permanently softens the metal, leading to the recession of valves and head bolts. My engine has avoided that by staying under 150C. Remove your tappet covers to see the colour of the metal just above the combustion chamber; light brown is okey, black is bad.