On the way back from ~50 km highway drive, I got a message "Transmission Failure" and "High Gearbox Temperature". The next morning, I found code P0705 (and cleared) but first decided to check the battery - it was very low but could still crank. Started the engine and found that the alternator was not charging, producing just about 12.5 volts.

Rebuilt the alternator (new rectifier, regulator and brushes) and charged the battery. After two days of disconnected battery, the message "High Gearbox Temperature" was still there. Started the engine and checked the alternator - very good ~14 volts now. I then did a hard reset, but the "High Gearbox Temperature" still persisted and engagement into R or D was a bit rough (didn't try driving the car). The strange thing was that, when in P or N, the alternator voltage (measured at the battery) was stable but, when I engaged R or D, I noticed some voltage pulsing looking at the interior lights and verified with a multimeter - the alternator voltage was fluctuating between 13.5 and 14.5 volts.

I then disconnected the battery and unplugged the TCU to have a look at it and connected it back again. Connected the battery and, suddenly, everything seemed fine. The "High Gearbox Temperature" disappeared and I had smooth shifts to R or D. Didn't test drive as it was late in the evening; will see how the transmission works tomorrow.

I now that low battery (bad alternator) can cause havoc in the car modules but the persistence of the "High Gearbox Temperature" after fixing the alternator (and after a hard reset), and especially that strange voltage fluctuation, puzzled me. Are these things "normal" occurrences after a low alternator (and battery) voltage episode?

 

I would suspect a combination of things has posted a trans code - bad Alt, low battery is as you know very upsetting to modules... I'm amazed there weren't more codes.
The pulsing voltage could be electronic limiter to trans?
The TCU needed total discharge from the memory or IDS reset to make the high gearbox temp go away. Which you did by unplugging it.
I doubt you'll see the fault again now you fixed the alternator.
It is an Odd One!

Run a trans adaptation procedure on it and see how it behaves.

 

Drove the car today and it shifted perfectly so I decided not to go through the adaptation procedure. How the TCU reset itself to normal operation (and the "High Gearbox Temp" went away) when I disconnected it and reconnected about 1 hour later, during which the battery was disconnected, is not clear to me. There was no power at the time of disconnection and no power at reconnection.

As for the alternator voltage fluctuation after its repair, and only in R or D while I still had "High Gearbox Temp", since everything in Jaguar X308 needs to "learn", I guess the alternator with new parts also had to learn again how to generate stable 14V.

Anyhow, interesting car...the X308...

 

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