So the basic gauge system described above works, but there are inaccuracies caused by ambient temperature (cold day vs. hot day), and variations caused by system voltage (low alternator output voltage vs. higher alternator output voltage. In order to compensate for those real world conditions, the gauges are a little more complicated than the simple system described above.
There are two "stages" to the compensated gauge. One of those stages is he simple gauge we already talked about above. The other stage is the compensating or regulating stage. It's job is to compensate for changes in ambient temperature and varying system voltage.
The compensation stage consists of another heating coil wrapped around another bimetallic strip. This bimetallic strip forms an electrical switch such that when the strip heats up, it breaks contact. And when it cools down, it re-establishes contact. The trick is, that it makes and breaks contact to it's own power source and the power source for the simple gauge stage.
The result is that this second strip/heating coil combo will make and break the power source such that it will always achieve the same average temperature. Of course the temperature is rising and falling some, making and breaking connection, but the AVERAGE is always the same.
Colder day? Power to the compensation strip will have to be on longer to reach the temp that bends the strip to the point where it breaks the switch connection. Hot day? Just the opposite. Power will be on for a shorter time.
Low system voltage? Again, power will have to be connected longer in order to heat the strip to the desired temperature,. And conversely, if the voltage is higher, it'll take less time.
The result is that the compensation stage creates an ON/OFF/ON/OFF pulse train whose duty cycle and frequency will change depending on the ambient temperature and system voltage. This effectively creates a voltage source that will always supply a constant amount of POWER to the gauge system under all conditions.
Clear as mud? Connect that constant power source to the simple gauge from above, and you have this:
If you put your key in and turn it to "ON" you should see the gauges start to rise. Don't start the car. Just pick a needle and watch carefully. You'll see the needle start to rise, but probably before it reaches it's final position, it'll pause... Then start rising again. Then pause again. This will continue until it finally reaches it's final position. And even then, if you watch carefully, you'll see the needle actually wiggles a tiny bit.
This effect can most easily be seen with a needle that's moving well above minimum like a full tank of gas. That pausing and wiggling is the compensation stage opening and closing.