I can now answer my own question.
The problem was the thermal fuse - a once-only thermal cutout. It is reasonably easy to replace. However you will need a crimping tool and some butt splice crimps (obtainable from electronic component stockists such as RS in the UK or Radio Shack in North America). They also stock the replacement fuses; you need to make sure they are rated for your mains voltage (110v or 240v) and for the correct temperature - for my machine it was 192C - it is written on the part.
You can get a repair manual on the web, e.g. at http://www.gbcconnect.com/assets/docs/DOC40P_95P_125P_PARTS.pdf . It is some help though not a complete guide.
To get at the fuse, proceed as follows - this is for the 125p but I imagine it would be pretty similar for the 40P and 95P.
Undo the 4 deeply recessed self-tapping screws that hold the front housing (part 3 in the exploded diagram in the Parts List) to the body of the machine. If the screws will stay in place, this will make it easer to reassemble later.
The front panel will now swing down; it will not remove because it is linked by electric wiring.
Loosen the 2 self-tapping screws that hold in place black plastic retaining lugs for the main PCB (part 8). Swing the lugs out of the way and slide the PCB upwards.
The white plastic plug-in connector for the thermal fuse is now visible at top left of the board, with 2 white wires coming out of it. Identify it by the word “Fuse” on the PCB. Disconnect it (it is a clip fitting).
Test the fuse with an ohmmeter applied across the bare conductors of the connector (there are 3 conductors but only the outer 2 are used – test across these). If there is no conductivity, the fuse has blown.
Remove the metal heat shield (part 28). It is held with one self-tapping screw and a plastic locating stub at each end.
Remove the top vent cover (part 31). It is held by 3 self-tapping screws and is going to be foul to get back on; again, if the screws will stay in place, that will make life easier later, but it's not very likely they will.
The thermal fuse is now visible, held in its fuseholder by a single countersunk self-tapping screw, and enclosed in some plastic sleeving, which you can just slide back.
Note that the replacement fuse must be crimped in place not soldered.
Reassembly is just the reverse of disassembly, but it is very fiddly getting the screws that hold the vent cover and front housing back in place if they have come out.
seglea, August 2011