What is the best sensor to use in a wearable device to monitor body temperature on a continuous basis: Thermistor, RTD or a semiconductor device?
In general, thermistors are the sensor of choice for measuring body temperature. They are sensitive, cheap, and their accuracy is adequate. After all, body temperature does not need to be measured to better than about 0.1 degree F.

With that said, measuring body temperature at the wrist is a losing proposition. There are simply too many chances for wrong temperature readings. The wrist, after all, is out at the end of the arms, with lots of opportunity for heat loss, and who knows what your hands have been holding on to. 

Another way to look at it is that all available sensors are inadequate - they measure the actual local temperature rather than the body core temperature.