Thanks guys for suggestions on this. Yes, you are probably right that the AMD processor of that generation run hotter. I have opened it up and got rid of dust, though there wasn't much.
It is doing it on both the FT and the Guardian, in both Firefox and Konqueror, and it also did it when rendering a large and heavily graphical PDF. So it is probably hardware.
One lesson of this is to be more careful about barebones in future. I thought of fitting a new cooler, but the problem is, there is so little clearance. Also, when you open it up, the airflow is clearly not the greatest because the case is fairly crammed full of psu and opticals. The main board is custom - this is the price of that nice compact form factor, so the natural lazy and cheap solution of buying a new mainboard bundle from Novatech is out.
Oh well, it was a good one while it lasted. There is another reason for changing it out, so maybe this is a good excuse. You young fellows will discover as you age, probably many years from now, a preoccupation which may be quite remote and novel at the moment. You find you cannot take for granted your continuing ability to manage technical things for other people. So one of the things you tend to do is, set up systems for them, and buy things for them, with half an eye out to the possibility that at any moment, they may find themselves on their own with it. As the Bible says, in the midst of life we are in death.
I am guessing that an i3 with lots of memory, Debian installed, clear simple instructions on keeping it up to date, well, it will give a few years... Best I can do, in any event.
Al