Why an oil cooler?
Air cooled motorcycles can run quite hot in some situations. This includes large amounts of throttle power for long periods of time; pulling a trailer or sidecar where a lot of engine power is needed; extremely bad traffic conditions; use of fairings in general (particularly fairing lower center pieces that are not ventilated). Engine cooling is obviously worse in quite hot weather. Your BMW Airhead engine has more than enough cylinder fins & head fins to dissipate enough engine heat in most circumstances, including some fairly extensive stop & go traffic, & modest speeds pulling a trailer or sidecar. But, there are limits.
For proper engine operation, lubrication, protection, etc., engine oil should operate in a reasonable temperature range after the engine has warmed up; not too cold, not too hot. The oil also needs proper viscosity over its expected temperature range in the engine. Usually, a multi-grade oil such as 20W50 is used in our Airheads. Quality 20W50 motorcycle oil is far better than the old single grades type of oils, & is quite adequate for most conditions, but a thinner oil might be wise if temperatures are at or below freezing; perhaps a 10W40. 10W50 and 15W50 oils are also available.