I have some 350W Fortron-Sparkle model FSP-350BU PSUs with empty spots
where a thermistor and fixed resistor would normally be connected in
series, and I'd like to know their purpose. I think that they connect
this way:

http://static.flickr.com/39/83308555_59e5e557a6_o.jpg

Capacitor C10 and pin 18 are on the small vertical circuit board
(beneath the removed fan controller board in the photo below) housing
the Fairchild KA3511DS PSU controller chip, and according to the
URL=http://www.ortodoxism.ro/datasheets/fairchild/KA3511.pdf]Data sheet
for KA3511DS[/url], pin 18 is the Extra Protection (EP) input, which is
supposed to shut down the PSU if its voltage goes high. In other
words, this seems to rule out the thermistor being used as an overheat
sensor because pin 18 is low anyway in normal operation.

Here are where the missing resistor and thermistor are located (circled
in red):

http://static.flickr.com/39/83310554_91d773cf62.jpg

The missing thermistor has nothing to do with controlling the speed of
the fan, and there's another thermistor for that purpose anyway (on the
heatsink, just above the screw).