The later +8s did have a tendency to run hot and the fan seems to come on for long periods of time especially on the 4.6L. It maybe the sensor is too sensitive and cutting in early or perhaps there is a restriction in the water circulation. Radiators can become blocked if the incorrect ratio of anti freeze/inhibitor has not be maintained. I would be inclined to flush out the cooling system and add new inhibitor to see if that makes a difference.
Neil
+1 and while it's empty of coolant fit a new otter switch, the temp sensor switch in the radiator, they are only about £20. On my 96 Plus 8 it was at the bottom corner of radiator, they are held in place by a metal clip and push into a rubber seal, you need to replace the seal at the same time. That should sort it out, the otter switches can be temperamental.