Edited by Zak Khan || Stepper motors like other motors deliver different levels of performance at different temperatures.
In fact, most stepper motors are designed to operate at relatively high temperature without issue — even to 90° C in some cases. However, undersized motors are at risk of excessive heat (not to mention sluggish acceleration if not total stalling).
One solution is to specify a larger stepper motor. Bigger motors keep cooler than smaller equivalents for a given job. The main caveats here are that larger motors can be louder; can transmit higher EMI and RFI than smaller options; are costlier than compact alternatives; and can have torque-to-inertia ratios than are sometimes prohibitive to speed.
Complicating matters is that current overdraw can also overheat motors. Read the FAQ: Aren’t heat and noise common stepper motor problems? for more information on this.
So when reading performance and torque curves, determine whether the curves represent behavior at room temperature or maximum rated temperature.
After assembly, a motor’s theoretical torque constant KT and voltage constant KE (as well as terminal resistance Rm) are fixed. However, actual values vary with temperature.
As temperature increases, so does resistance — just as the torque constant and voltage constant decrease. A simplified graph below shows how a motor’s performance can change at elevated temperatures.
Notice the decreased performance as the motor temperature rises:
Rth = thermal resistance
Rm = Motor terminal resistance
Irms = Root mean square current
θa = Ambient temperature, and
θm = temperature of the motor.
Note that this provides the increase in temperature internally. It’s impossible to tell how much hotter a stepper motor has become simply by feeling its surface. Not only can this be dangerous (because motor surfaces can get hot as well as pose electrical hazards) but it’s also a misleading technique — because motors are insulated to prevent them from becoming hotter than allowed by applicable safety standards. This means that a motor can either feel quite hot yet be running perfectly fine or — even more deceptively — insulation makes it feel as if nothing is wrong. When in doubt, consult manufacturer documentation and ask motor-maker application engineers about allowable motor operating temperatures.
More information on stepper-motor temperature ratings and effects
Side note about the relationship to stepping mode and motor heat
Note that full stepping a two-phase motor with the phases fully on together outputs more torque than running that same motor at the same maximum current per phase in half or microstepping. That said, running the motor at higher peak current (×√2) with a half or microstepping waveform delivers the same torque for a given level of power consumption as full stepping — but for smoother output motion without any extra heat generation.