As others have said, different types of magnet wire have different temperature classes of insulation. They can be rated for anywhere between 90 C and 240 C. You won't be able to tell what kind of insulation the magnet wire has by looking at it. Your best bet is to look at the nameplate of the motor and look for an insulation class. It might be an actual temperature like "180 C" or it could be a letter code like A, B, F or H. A, B, F, and H are the most popular insulation classes and have rated temperatures of 105 C, 130 C, 155 C, and 180 C, respectively. If you can determine the thermal class of the motor, then that will be the minimum that the magnet wire will be rated.
Even if you can figure out the rated temperature, that won't be the temperature that it burns up. When wire manufacturers rate their wire, it is based off of an accelerated test where they apply a voltage in order heat up the wire. They do this on 3 samples with 3 voltage and therefore 3 different temperatures. They measure the time in hours, plot the 3 points and then extrapolate the 3 points to the 20,000 hour temperature. That 20,000 hour temperature is used to rate the wire insulation.
But let's say the 20,000 hour temperature is 100 C. You could raise the temperature to 110 C and the wire won't burn up right away ... it might still last 10,000 hours. And you could raise it another 10 degrees to 120 C and it still won't burn up right away ... it might last 5,000 hours. The wire will eventually fail at all these temperatures but the real question is when. Raise the temperature high enough and it might fail in 2 hours or 1 hour or 10 seconds.
Assuming you can figure out a temperature, also keep in mind that motors don't heat up evenly. You can get hotspots on the windings and you generally won't know where those hotspots are located. Typically when you place a thermal protector or thermal sensor, you assume you are NOT on one of those hot spots and that your highest winding temperature is 5-10 C higher than what your sensor tells you.