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Oh wait, ...
You want to only feed coolant to the gearbox when the engine is already warmed up, but limit the temperature of the gearbox to about 80 degrees C....?
So you need TWO thermostats.
And as normal wax thermostats OPEN on temperature rise, then this gets quite complicated I think, because really you want one of them to close on temperature rise. You could rig one to open a wide 'bypass' on temperature rise I guess, but that's complicated.
Alternatively, you could use a single 2-port motorised zone valve from a central heating system, which gets its OPEN signal and its CLOSE signal from two thermostat switches, so it is only open between your two desired temperatures. You could use adjustable thermostats so you can tweak the switching points.
(You'd have to find 12v motor/auto versions of these controls, or else use a small inverter, ...but we're only talking an amp or less here.)
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