Actually, the oil cooler is the primary source for "oil cooling" on the 961. Increased oil capacity helps but to a very, very minor degree because a cup more or half a quart more isn't going to cool anything down. Once the oil is hot, then it's all "hot" until something cools it down. I won't go too far down with the explanation, but more oil doesn't actually mean better cooling in most cases if nothing cools it down. The idea behind oil level and cooling is to make sure it stays within the proper range of viscosity.
If you didn't have the oil cooler, the oil would remain at relatively the same temperature as the oil entering tank would be as hot as all the oil in circulation.
You have to look at the oil in the frame design. On a 961 the oil tank is heated as well by the rising engine heat, so that's also adding heat not cooling it. The oil tank is surrounded on three sides by the gas tank, and there is very little airflow. Bourget did this with his bikes, and they ran hot as well, even with a cooler
Look at the Harleys. Oil filters in the airflow and those that have them, oil coolers in the airflow. Even the oil bag(tank) is out in the open to help with cooling but it has air circulation on almost all sides.
Keeping the oil pump circulating properly, proper flow, etc, all work to keep the oil temp where it needs to be.
On the other hand, low oil means the same oil must now make more passes through the system without a proper cool down that causes the oil to break down faster. This is even more critical on bikes that have oil sumps versus tanks. The oil sits in the bottom of an already hot engine, then gets cooked via the clutch friction, etc, which is why many prefer a separate engine, primary, gear.
This is why I've stressed looking at your oil tank output and the way the oil pump intake hose is routed, the inline filter, etc from previous posts