The electronics control the temperature of a mirror using the Peltier cooling device you found. Light is directed on to the mirror, and when moisture forms on the surface, at the dew point, the reflectivity changes sharply. The mirror temperature is usually cycled, so that the rate of change of reflectivity can be detected. This is supposed to minimise the effects of any, inevitable, contamination of the mirror. The sintered filter in the photo also supposed to help this.
Contamination is always a problem, though.
C accuracy on dew point achievable. They are still made Michelle Instruments of Cambridge being one manufacturer. The temperature sensor may be a resistance thermometer, to give greater accuracy. My first thought was that it's something like an LVDT position transducer, but I don't think this is the case. There are two coil forms, each containing two series windings of fine enamelled wire, with a 1.5mm hole through the middle of them.