Is the bottom of the fairing between the headlight and the engine flat like the vetter or rounded to allow the air to flow up the sides rather than directed onto the engine surface area?
Certainly, the lower the air temp, the more heat it will accept from the engine cooling fins as well the entire outer surface area of engine unit.
However, the quantity of the air making contact also makes a difference.
Maybe think of the air as a bucket brigade for heat removal. Hottter air has smaller buckets than cooler air. But, if you use more buckets, you can still remove the same amount of heat from the motor unit.
Ive said before that relying on the oil to cool the SOHC4 motor can only bolster about 5 percent of the cooling capability inherent in the engine design. Surface area for the heat to leap off from, is a dominant factor in the heat exchange process. That and the volume of air passing over and accepting the heat to be taken away are what cools the motor.
Oli coolers are to help extend the life of the oil integrity. Certainly, that can help with proper lubrication and friction reduction. But, cooling the motor overall is only a minor contribution from an oil cooler. If you can keep the motor cool, it won't heat the oil.
Cheers,