Hi Glyn Finch,
I bought my tractor (Satoh ST2020) in 2005. Since 2005 I am using 10w40 STOU oil for the tractor. Unfortunately I don't have any manual for the machine, so if you have more precise information, please let me know.
STOU oil is suitable for both motor and gear box. As I remember it is needed ~20 liter of oil by the gear box and other 4 liter of oil by the motor.
By the way I have the same symthom as you. It can be suspicious the cooler/radiator (use only distilled water for it) or the heat detector.
I had earlier the same problem, but at that time the outer surface of the radiator was coverd by cottonwood. Check it and clean it if it is necessary!