Update to the update, I finally got around to replacing the temperature sender, not a nice job. I bought a set of JIS screwdrivers, but quite a few fasteners had already been chewed up. I had to drill a few out, it would have been easier with the main tank removed but I kept it propped up. I got a replacement airbox off eBay, I was too enthusiastic with the drill, and made a good one up from the two, and I have spares in case the problem happens again. I didn't want to remove the throttle bodies so I had to skin my knuckles to remove the electric connector and unscrew the sensor. The old one was clearly past its best, all corroded apart from the tip. Anyway, I've put it all back together, I have no bars from cold, and my fuel consumption is back to normal. I had to sit in traffic today and it went up to four bars, but down to three once I started to move, so it seems the problem is solved now.
I don't know if one problem led to the next, but if you are repairing one problem then it's best to be prepared to do them both, after several years immersed in coolant the sensor will probably show signs of corrosion.