Well the answer was air con relay.
When I took it in his diagnosis (main dealer but only father and son operation) was it will be your alternator. They are expensive- about 170 euros.
Next day popped in. Think it is this 240 invertor which we use maybe once in three months. OK disconnect that see if that cures it. It isn't your alternator.
Following day popped in. Think it is the radio. I am feeling quite despondent by now.
Following morning. No it isn't the radio. We don't know what it is. Went back that night thoroughly expecting to have to extend the car hire. But no, they had found it was the air con relay doing something wierd on switch off.
Now for something really wierd.
Two days before this problem manifested itself , we were unlaoding the disbaled mother in law near a place we were going to. I left the car running , air con on flat out, in the street. There was a sudden very loud hiss from the bonnet area possibly accompanied by a cloud but afterwards we couldn't be sure. Too preoccupied with the MIL. I just assumed the air con had discharged all its gas through a catastrophic leak.
On way home air con worked, no water temp problem and no water loss when I checked level next day. The guy at the garage said the air con gas might have been over pressure and some blown out via a valve. Is that possible? It had its bi annual recharge (empty and the same amount as last time put back in.) about a month ago.