I feel like I've made a mistake, but love the bike now.

[Water Warrior 2]

Seems to me that the oil supply line for an oil cooler is attached to the engine where a oil pressure gauge would screw in to check oil pressure. There was some discussion as to whether the added line would actually reduce the oil pressure during regular operation. That in itself is a reason for more in depth investigation of an oil cooler.
A larger oil pan with cooling fins might be possible without any oil PSI reduction. Even an extra half liter of cooled oil might make a world of difference in a hotter climate. Could be a good mod that is maintenance free.