What does the term Maximum Operating Temperature (Tmax) mean?

The maximum operating temperature is exactly as it sounds, it represents the maximum temperature at which a particular type of magnet can operate before it becomes permanently demagnetized.
All permanent magnets weaken in proportion to their temperature coefficient, but as long as the maximum operating temperature is not exceeded, this can be fully recovered on cooling. If the maximum operating temperature is exceeded, the losses are not fully recovered on cooling. Repeated heating of a magnet above its maximum operating temperature and cooling significantly demagnetizes the magnet.
Neodymium magnets work best at cold temperatures down to about -130C. Normal neodymium magnets retain their magnetism at operating temperatures up to 80C, while different variants of neodymium magnets can operate up to temperatures of 230C.