As to fluid friction, it's a law of physics but is likely only contributing a little to your heat problem.
IMO, 150F would not be problem. It's when you are exceeding about 210 is when it gets to be a problem. 210F is the point at which the viscosity numbers are determined, so at that temp, the oil is within the viscosity range called for by the grade designation (90 110, 140, etc.). Cooler, it's thicker. Hotter it's thinner. If the temps are exceeding 210F by a significant amount, it may well be thinning a lot. Knowing the operating temp would help you to choose a better oil. If it's exceeding 210F, you'd want that 140 grade oil.
Another thought: I have a PTO driven Woods chopper that has a 90 degree gearbox like yours. A few years back, I was chopping down wheat stubble and after a few hours, I noted more noise. I found the seal had blown out of the lower part of the box and all the oil had drained out. I added some oil but it was still noisey and it leaked out pretty fast. I muttered a few expletives, thinking the gearbox was smoked, got the seal, noted there was no excessive play or externally apparent bad bearings, tore it down enough to replace the seal, figuring I'd finish the field and overhaul the box as a winter job. I found I was out of the "regular" gear oil I use in the farm stuff (chopper, ditcher, auger, etc) but had some extra Lubrication Engineers LE 607 from a truck project, a straight 90 oil with lots of a moly type additive. I put that stuff in and when I went back out.... noise gone! Remarkable! I spoke with an LE guy about it and he said this was a common story. I also can report that the LE607 reduced rear axle temps in my diesel pickup (vs regular mineral oil) as much as a better known synthetic did. Unfortunately, LE607 is no longer available but Lubrication Engineers (Google them) has a replacement. I doubt an oil alone is going to cure your problem, but it might be worth looking for a very robust oil when you find an upgrade for your gearboxes.