check the gearbox and T-box transfer levels.  However, you very likely have
a cat under there as well... and they get hot.

There should be a warning light, I should think, for transmission temp., if
it really gets hot.

Best to switch off HTML posting as it looks a mess in many people's
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the relevant protocols.

My 110 has been like this for years, more to do with air being able to
come up from under the car than any real concern has been my
assumption, as a gearbox and transfer box are going to get bally hot
anyway as part of their normal function.  Some cars have specific
cooling systems for preventing this, but it's only really needed on
high-performance cars or those with particularly stressed
transmissions, I'd imagine that large trucks probably have
transmission coolers for example.

I've always regarded that as perfectly normal, you'd get hot too if
you had lots of gears thrashing about inside you at high speed!  Mine
only gets hot when cruising, at similar speeds to yours, I'll be
solving it not by trying to fix the transmission problem (because I
don't think there is a problem) but by fixing the leaks around the
metal plate that sits under the cubby box which I caused by bolting
the cubby box to the thin plate instead of doing a proper job.

If a gearbox gets too hot it'll sieze, and mine's not done it in a few
years with those symptoms despite cruising for 3 hours a day at an
average speed of 60MPH while I still commuted.  I don't do that kind
of driving any more but the landy didn't seem to mind it.  In the
summer it did get uncomfortable and I had to open the windows at
times, not even the draughty old canvas roof I fitted could get rid of
the heat.