Smouty, it could be a couple of problems beside the computer itself.
Since the car starts well, then goes bad, and finally you can make it good again by running it hot, I would suspect the lambda sensor (oxygen sensor) to be bad. A garage *may* be able to diagnose that by putting the tester on. Otherwise just replace it!
I'm not sure about the gearbox problem, but since it helped slightly to clean the connectors on the engine ECU, I suggest you go through the struggle to get the gearbox ECU out for a connector cleaning.
I'm taking my 24v to my local Mr Transmission
(it's the name of the garage!) next week for a gearbox oil change, and I can ask what he would do. Oil change on these gearboxes is not prescribed in the service book, but I would never run it without doing so. This is a very reliable gearbox (a ZF unit, also used in Mercedes Vito), but oil that has been run hot kills it.
Oh, yes the box. It's a canister for filtering toxic gases from the return fuel. It cannot affect the way the engine runs.
- Anders