Hot and cold safe stall times describe the same locked-rotor thermal limit, but measured at two different reference points along the motor's heating curve: hot is the time the windings survive a stall after the motor has been running at rated load, cold is the time the windings survive a stall from ambient temperature with no prior heat input [S1][S3]. The cold value is always larger, and the hot/cold ratio is typically 0.80 to 0.90 for standard induction motors [S4].
Because the relay has to make a binary trip-or-run decision in real time, the practical question is not "what is the limit" but "where between the two limits do I place the overload curve, and how much hot-start margin do I leave for repeated jogging duty?" The answer depends on starts per hour, load inertia, and whether the motor is governed by NEMA MG-1 or IEC 60034 thermal limits [S2][S4].
What hot and cold actually mean in the thermal model
The hot condition is reached when the motor's thermal capacity used value is at or near 100% from prior running, and the rotor/stator have stabilised at operating temperature. The cold condition is reached after the motor has been de-energised for a time equal to or greater than its cooling time constant, usually 4 to 6 times the machine's thermal time constant τ [S1]. For a typical medium-voltage motor with τ around 30 minutes, the cooling interval to reach a true cold state is 2 to 3 hours [S2].
Another manufacturer example quotes 3 cold starts versus 2 hot starts from the same locked-rotor thermal envelope [S5]. These ratios are not arbitrary; they track the I²R heating that has already accumulated when the motor is commanded to start from hot [S3].
Where to place the overload curve between hot and cold
The thermal model in a modern motor protection relay runs continuously, integrating heating current and subtracting cooling current against a 100% thermal capacity used (TCU) reference. Trip occurs when TCU reaches 100% during stall; restart-inhibit is released when TCU drops below a settable threshold, usually 10-30% [S2]. The safe stall time the relay actually uses as the integrator time constant must be set close to the hot value, not the cold value, because if the relay is configured with the cold time the motor is allowed to run longer than the winding can actually tolerate from a hot start [S4][S6].
The overload curve itself (the inverse-time characteristic that trips on running overload, not stall) is placed between the hot and cold curves, biased toward the hot curve when the process has frequent jogs or high inertia [S6]. Setting the curve at the hot boundary plus a 10-15% safety margin is common for pumps and fans, while conveyors and crushers with elevated load inertia should sit closer to the hot limit with no extra margin [S2][S3].
Jogging factor, 5000-start fatigue budget, and where the relay enforces it
Every start consumes a portion of the rotor's mechanical fatigue budget. NEMA MG-1 and the IEEE 841 references commonly cite a 5000-start cumulative design life for standard squirrel-cage rotors, after which the rotor bars and end-rings are considered end-of-life for cyclic stress [S3]. The jogging factor JF, defined as the ratio of the motor's permissible starting time to the actual measured starting time, controls how many starts per hour are allowed.
Relay implementation: frequent-start supervision counts successful starts within a sliding window, typically 1 hour or the motor's cooling time constant, whichever is longer, and inhibits the next start command when the cumulative thermal cost of the prior starts would push TCU above the stall limit [S2]. External tacho switch feedback is required when starting time can exceed the safe stall time, because the relay needs a confirmed rotation signal to know the motor is no longer in stall [S2]. Without that input, the relay has no way to distinguish "stalled with locked-rotor current" from "accelerating with near-locked-rotor current" until the thermal relay integrator trips. Practical engineer's note: the tacho input is the cheapest insurance on any high-inertia drive.
Comparison: settings for three real load classes
Pumps and fans, low inertia, few starts: cold stall time can be used as the integrator reference with the overload curve biased toward cold. These machines rarely exceed 2-3 starts/hour and have accelerating times of 3-8 s, so thermal margin is not the constraint, mechanical wear is [S2].
Compressors and conveyors, medium inertia, intermittent jogging: set the integrator at the hot safe stall time, and place the overload curve between hot and cold at roughly the 50-60% point. Typical starting time 8-15 s; allowable starts/hour 4-8 depending on duty cycle [S3][S6].
Crushers, mills, large fans with blade pitch, high inertia, repeated jogs: integrator set at the hot value, overload curve set right at or just below the hot limit, and frequent-start supervision must be enabled with a low TCU-inhibit threshold (often 20%) [S2][S4]. Starting time 15-30 s is not unusual; a 3-time hot / 5-time cold rule is the practical ceiling before the rotor fatigue budget is consumed prematurely [S3].
Failure modes when the setting is wrong
Setting the overload curve above the hot limit on a high-inertia load invites winding insulation damage within a handful of hot-start events. The relay will not trip because the integrator is still within the band, but the cumulative I²R exposure has already exceeded the machine's thermal limit [S2][S4].
Setting the overload curve below the cold limit on a low-inertia load causes nuisance trips during the first start after a long stop. The relay sees the inrush current, integrates it, and trips before the motor has had time to accelerate, even though the machine is well within its thermal envelope [S1][S6]. Operators respond by overriding the relay, which removes the protection entirely. The fix is to raise the curve toward the cold limit and re-enable the thermal lockout at the right TCU-inhibit percentage. The motor protection relay cannot help if the operator is bypassing it.
Interaction with built-in thermal sensors and the protection hierarchy
Built-in thermostats (PTC thermistors, Pt100 RTDs) are considered "unstable protection" against stall and rapidly changing temperatures; they respond to the embedded sensor point but have limited coordination with the relay's own thermal model [S7]. Best practice treats RTDs as a backup trip at a higher temperature (typically 130-155°C for Class B/F insulation) while the relay's inverse-time curve handles the primary protection for stall and running overload [S2][S7].
For locked-rotor events specifically, RTDs are too slow: the rotor and stator reach critical temperature within 5-15 s of stall, while the embedded sensor's thermal mass means the RTD reading at the slot is still rising during that window. The relay's I²t integrator is the only element fast enough to catch a stall inside the safe stall time [S2]. The protection relay family in general uses current as the proxy for heating when the speed of the event rules out direct temperature measurement.
Verifiable signals to track
Two trackable items for the next quarter: (1) IEC 60034-1 thermal-limit updates referenced in the latest IEEE PCIC papers, with the 2022 Schweitzer Engineering / Phillips 66 paper still the most detailed published guidance on hot/cold integrator placement [S4]; (2) the increasing use of RTD-assisted thermal models in newer relays, where the relay back-calculates τ from measured temperature and adjusts the safe-stall integrator on the fly, instead of relying on a fixed curve. Engineers commissioning a new drive in 2026 should ask the vendor whether the relay's hot/cold limits are user-settable or learned in real time.
For related protection work, start-inhibit thresholds on thermal capacity used is the next setting downstream of the overload curve, and the diagnostic flow when the motor protection relay will not trip on overload usually traces back to a curve placed incorrectly between the hot and cold limits.