So that is probably the most arduous condition you could give - zero air movement across it (which would be the same regardless of where you mounted it with a similar testing condition) so undoubtedly the fan, lights on so a significant load - 140F is not horrendous - ~ 60C and even modest airflow across it (and bear in mind you will almost NEVER be sitting idling with the fan running for 12 minutes when riding! - consider that your engine itself is at 100 C in this condition) will get that to a healthier level. As we discussed in PM, (& as you mentioned above) yes, at the least however the unit needs to be turned 90 degrees, so that when bike IS moving air flow through the fins will aid that.
I see you are reluctant to modify the airbox - how about the fender? If you were to trim the very bottom, it could slide further back?
How about removing the original bracket from the fender and mounting it in the vertical (well off-vertical actually) plane on the fender?
If you like and can plan a visit over my way, I can help you figure out a good solution - I have connectors and even those Furukawa terminals on-hand if any wiring extension/reconfiguration is required.
I'll be working on DJ's bike this weekend (installing key-less system) so will take a good look at what might be other viable options for location.