For squirrel cage induction and synchronous machines, the limit is NOT the stator winding temperature. It is the temperature at the rotor-bar-to-shorting-ring joint. And of course this is almost impossible to measure accurately - especially in a "on the fly" in a real life situation. With enough knowledge of the machine geometry - including number of bars, bar material and cross-section, ring material and cross-section, joint type (butt braze vs lap joint vs through joint), driven load inertia, motor rotor inertia, actual applied voltage at motor terminals during the start attempt - and so on, it is possible to mathematically determine how hot that joint is going to get.
There is no really good relationship between stator winding temperature and joint temperature either, in most cases. At least, not one that can be used as a rule-of-thumb across multiple ratings and manufacturers. This is partly due to the insulation on the stator coil (which is between the sensor and the actual conductor) and partly due to the difference in conductor cross-section. The nonlinearity gets worse when the material of the coil conductor is not the same as the bar and/or ring, too.
One other thing to note: if the machine stops turning completely, the actual temperatures are going to RISE for some period of time (even without any current flowing) because the method of cooling has suddenly become far less effective: what used to be convection plus radiation is now radiation only.
IEEE, IEC, and NEMA all say "read the motor manufacturer's directions regarding attempted starting".
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