A bit more info as I've trawled the web:
http://www.toyota-supra.info/forums/mkiii-faq/1043-auto-trans-oil-change-made-easy.html
Basically you should NEVER flush the fluid in an autobox unless it's new.
Ours are not new so they should never be flushed.
The reason is that a flush releases too much dirt in one go; which clogs up the oilways, valves etc.
The way to clean dirty fluid is to do a drain and fill on the gearbox sump only (about 40% of the total oil) on a regular basis which will gradually and safely clean the whole box.
I'm not sure if dropping the pan is worth it on a metal mesh filtered box, I'll pop my USB endoscope in to have a quick look at how clean the floor of the pan is and only take it off if it's dirty or a solenoid needs replacing. Dropping it will need a new gasket etc and it's quite messy.
BTW I also found what the codes for the gearbox means:
30-40LE
L = Lockup (Locks up the torque converter if conditions permit)
E = Electronic. Basically the manual level selects possibilities and the solenoids select the gear.
the gearbox is a 3 speed auto to which they've added an overdrive (another planetary gear + clutch) and lockup.
2 Solenoids select gears 1 2 3 4
1 Solenoid for the lockup
1 Solenoid for the overdrive
This seems to be one of the best discussions on it:
http://www.pirate4x4.com/forum/toyota-truck-4runner/587521-a340-transmission-issues-faqs.html#/topics/587521?page=1&_k=7dlrrc
You can see the internals (minus valve body) here:
The 3 pots in the top-right corner are to make the changes smooth, the piston + band top centre is an actuator + brake band, the pistons for the clutch packs are concentric to the shaft and very short, fat things you can just make out on the cutaway in the 'how it works' link.
And here's how it works, I think it's actually the A340 box he's got cut away there.
https://www.youtube.com/watch?v=HcNH9AFWaNI
Oh, and if a gearbox has a lockup and the lockup fails, it can overheat because the lockup reduces the heat output quite a bit - so a persistent overheat could be down to that. (See
https://hiace-super-custom.forumotion.com/t3030p75-worth-keeping-my-hiace#16222)Toyota/A340E Wiring diagram (from Supra forum)
http://www.turboninjas.com/mk3supra/tewd/Flyout-2.jpg