The oil temperature gauge in the cockpit shows the temperature of the oil...
Refer to figure.
Engine oil is required for lubrication, cooling, and cleaning of an engine. These are essential purposes anyway, but monitoring engine oil pressure and temperature are also the best two indicators of engine health from within the cockpit. Oil temperature in particular can tell us about potential cooling issues or damage within the engine which is causing abnormally high heat output, and can even indicate that the oil quantity may be getting low (due to a leak) if an oil quantity gauge is not fitted.
The oil temperature gauge is often fitted after the oil cooler but before the extremely hot engine parts. You don't want to measure the oil temperature directly within the engine as you would effectively just be measuring the metal temperature, and you want to have a better idea of the temperature of the bulk of the oil. However, we also do not want to measure the oil temperature within the reservoir as it could become uncovered in the event of an oil leak and stop providing indications. It is usually located somewhere after the oil cooler (which either is after the engine itself or after the sump/reservoir, depending on the system).
Whichever placement is chosen, it doesn't matter for this question, all we need to know that is is NOT in the hot section of the engine (that would unduly affect the oil temperature and not show us what we need to see), so is some point after the oil cooler, and not inside the reservoir itself (as previously mentioned).
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