Making a relatively good temperature sensor is easy and cheap. Unfortunately, the sensor measures its temperature, which is very often something completely different than what is intended to be measured. Measuring the core temperature with a wrist-worn device is very difficult.
Let's take cross-country skiing or running in the winter. The environment is at –15 °C / 5 °F, and I need to make sure the watch is covered by gloves and sleeves to prevent it dying from hypothermia (and even with those precautions two hours is a long time). In the beginning my fingers are extremely cold, after maybe twenty minutes they start to feel warm indicating much improved blood flow in superficial vessels. If I get it right with the clothing, my core temperature should not rise too much.
I cannot imagine any way to measure the core temperature from the wrist in these conditions.
The same applies to nocturnal body temperature (which would probably be quite useful). During these hot summer nights, my skin temperature is high, as my body tries to get rid of extra heat. During the winter, the temperature depends very much on whether my hand is under the duvet or not. The skin temperature is a great indication of whether I feel cold or hot, but it does not tell much about the core temperature.
On the other hand, the absolute core temperature might be interesting, but it is a very personal thing as a health indicator. My base temperature is quite low, as is my heart rate (I cannot use the low HR alarm of AW, as my night time HR is usually below 40 bpm). So, for me 36.5 °C (98 °F) is already an indication of something strange going on in my body, whereas the same temperature would be low for someone else.
I am not saying the skin temperature measurement would not be useful. With clever algorithms it could be useful in specific applications — such as ovulation detection — but it is not generally a good health indicator. Last time I had fever, it was some variant of the season's special. My rest rate went up by 20 BPM, which is much easier to detect by a watch (and I did not feel well at all), so the thermometer wouldn't have added anything.
Knowing the real core temperature would be very interesting even from the scientific point of view, and having continuous real time measurements of the core temperature would probably open up a lot of new possibilities. For example, I would be interested in knowing my body is not overheating when I run in hot and sunny weather. That would make longer distance running safer and more efficient. Unfortunately, the most reliable way of making such measurements requires a jar of lube and a bead-shaped sensor.