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Thanks for the re-cap Daox.
Check and double check of course, but I really doubt the transmission will be troubled by running a bit hotter than 180F (82C). I'd imagine it would be more than happy to run at 100C (212F).
The way I see this temperature issue with engines (and gearboxes are similar) is thuswise...
Vehicle engines have been designed to run at about 92 C simply because that is just comfortably below the boiling point of water.
Water happens to be one of the very best coolants available at any price, but only in its liquid phase. Even minor local boiling in cylinder heads can be very damaging, hence running engine coolant systems under moderate pressure to raise the boiling point a bit. But basically a nice, nominal 10 degrees below boiling point is a good safe temperature to aim for.
There's nothing inherent in the materials that engines are made of that makes 92 degrees C a particularly good temperature to run at, EXCEPT that it is just comfortably below the boiling point of water. Those people who have used Evan's Waterless Coolant, which has a boiling point of about 180C (360F) have had good results from raising their engine temperatures by several degrees. I think it's fair to say that higher temperatures are better for engines in general, provided that the temperature is relatively even. Overheating is really bad, but not because things get too hot in an absolute sense. When the temps rise above the boiling point of water then the heat dissipation mechanism breaks down in a catastrophic way, with local boiling in cyclinder heads that 'runs away' as those spots are no longer in contact with water, but only steam, which is a poor conductor of heat.
As I understand it, synthetic engine oil doesn't even begin to break down below about 150 degrees C (300F?). I did a little research on that when I was contemplating fitting a sump (oil pan) heater, and was concerned that a powerful sump heater pad might locally overheat the oil in the sump. I would imagine that synthetic gear oil behaves in a very similar fashion, and that therefore the practical temperature limit for a gearbox is 150C. Unlike engines, gearboxes don't have localised hotspots, so I'd imagine they are more tolerant of elevated temperatures, although they don't normally get regular oil changes, so any gradual heat-degradation might accumulate over a period of years. Still, running at 100C for example ought to present no problem at all.
The hotter the gearbox, the more heat will be transferred down the driveshafts to the wheel bearings and so on. Win/win/win, as far as I can see.
As for "active cooling", well if you are happy with a temperature of about 100C, then the gearbox will be actively cooled by the coolant running through it, through the engine block, the cabin heater matrix and the radiator.
But as the car is driven, heat is naturally transferred from engine to gearbox anyway, just through conduction and air convection, so if you can start off the day with a warm gearbox then maybe you can rely on the existing heat transfer from the engine to keep it warm. If you can plug into the mains at home then maybe all you really need is a gearbox heater pad.
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