As David says first series cars just the one thermostat, the wax type fitted in the radiator.
Second series Aprilias have
two thermostats, the standard wax one in the top rhs of the radiator plus another in the top radiator hose, see the attached TAV of a second series radiator. You can get reproduction 2nd series thermostat housings from Italy, I hate to think what the cost might be though.
I put this story on my web site a few years back regarding my radiator and cooling experiences.
http://www.narrywoolan.com.au/home/The_radiator_saga.htmlI have shutters and a working wax thermostat. Since the above the only cooling issue I’ve had is getting the engine hot enough on cold days, she struggles to get above 60 deg C. On warm days in traffic and steep mountain climbs she sits comfortably around 70 - 75 deg C.
However if you have an overheating problem I would be looking at the radiator first to see if any of the tubes are blocked, then take the water pump off and check the internal channels fixed in the bottom radiator tank are there, if not the water cannot circulate correctly. Next the water pump, they can corrode horribly, and I found mine was missing the spacer at the end of the impeller (p/n 38-4041), which meant it wasn’t engaging with the pulley. Also the slot in the copper tang, the part with the left hand thread that the fan screws on to, (p/n 38-4060) can wear which also means the impeller isn’t turning.
New water pumps are available also in Italy, again at a price! Many owners have fitted a normal thermostat like the motor cycle one mentioned, maybe they can come forward with their experiences.
Oops, re read your post and realise your problem is not overheating, please disregard the above!
Noel