Do you live in a particularly hot climate? I ask because a KZ650 wouldn't normally need an oil cooler except maybe for a racing application. If you do run an oil cooler you should consider installing a thermostat to ensure the engine reaches and maintains an appropriate operating temperature, otherwise you may end up with condensation in the oil. Ed
Our climate is continental, we have quite severe winters and warm summers. However, all three of my air cooled "inline four" motorcycles (Kawasaki Zephyr 750 and two projects based on Yamaha XJ600 51J and Honda CB750 RC42 engines) equipped with factory oil coolers . I also registered no issues with condensation in oil not for all my mostly 100K km experience with Zephyr 750 nor during tens of thousands of kilometres on other air cooled bikes. Lot of that kilometres I rode when temperature was less than 10C or even slightly below 0C.
On the other hand, oil cooler is mighty useful in tight city traffic and when days are really hot. I definitely never have had an issue with overheat, even when one of rides on Zephyr ended up with hole burnt in one of pistons.