Well, I think there are two issues here. If the external temperature sensor is giving simply wrong readings, it should be replaced. Certainly it'* easy enough to swap it out and see if the replacement gives the same temperature readings.

However, if the air conditioning is slow to back off inside the car -- I mean that it cools _too_ much, and doesn't stop cooling until the interior temperature is definitely below what was set, which is how the original poster described it -- then the problem is with the _interior_ temperature sensor not responding.

In older Bonnevilles, this can happen due to dust and dirt buildup on the sensor behind the intake grille in the dash. It sits within a vacuum stream of intake air (there'* a little hose behind it to draw in cabin air over the sensor), and as such it gets covered with dust and dirt over time, which serves to insulate the sensor from the air temperature that it'* supposed to measure.

Interesting info about the internal temp sensor. I knew it was in the location you spoke of, but didn't know there was a little vacuum hose that draws air back there. Interesting!

I think its official name was something like "aspirator tube" in the service manual (I should go back and look; I may be mixing that up with the tube from the old AIR pumps that fed air to the catalytic convertor), but generally it'* called a "sniffer"...