You ask specifically about what happens if a temperature exceeds a certain temperature. The answer is (like in a lot of other cases): Look in the datasheet. Usually you will find a value called "absolute maximum ratings": You can't really know what happens if you exceed these values. Your chip might take an internal damage (this can also mean: reduced performance), or the case might melt. Do not go there, so you don't have to care how exactly the chip will take damage or fail.
Other than that, there is the operating temperature range, where the manufacturer guarantees the accuracy of a part. Always chose your sensor so that all expected temperatures where you want reliable measurements are in that range. Notice: Sensors usually are more accurate in the middle of the measurement range, manufacturers will sometimes tell you in their datasheet:
So what sensor should you then use? In every case you have to answer these questions (maybe another more):
- Will this sensor handle the temperature? Will it be accurate enough?
- How do I read the sensor value? The DS18S20 can be read via 1-Wire interface, a "naked" NTC will need some circuit around (just like a thermocouple).
- In your case: How will I mount the sensor, can I solder it
The NTC you choose will not be very accurate at this temperature, as the resistance changes only a little per degree at high temperatures. As this document says (p. 27), thermistors are somewhat sensitive to overtemperatures. You have also to look for a method to read out the sensor and calculate the temperature (NTCs are non-linear).
You will also have to think about how to connect the sensor to your Arduino (soldering is not an option, you might have to crimp or sth. similar).
Considering this, I would go with the answer from Majenko: Thermocouples are good at measuring high temperatures (the accuracy under 100°C is not important to you, I guess) and they come with their leads already properly attached. If you combine this with the IC Majenko named, you don't have to mess around with calculating the actual temperature or how to do an A/D conversion. You might only be careful about the different types of thermocouples and chose the right thermocouple/IC combination.