For those equally frustrated that the 350e doesn't have an external temperature gauge, I finally have some news. 4 weeks ago the car went back to the dealer as they also couldn't understand why such a basic feature had been excluded from what seems to be UK cars only. Yesterday I received the news that there is now a software update for the car so that we can see the temperature.
The car is booked to go back in for the software update on the 7th Dec, so I will keep you posted. At the moment the dealer doesn't know where it will appear on the dash, I'm hoping in place of the Kph on the bottom left, but we will have to wait and see.
When it is done and I have more detail I will post a photo, armed with this photo you can then use this to approach your dealers to get the software update too.
This is potentially great news as I have found it so daft that this basic feature has been omitted.