There are challenges for a servo motor's protection against overheating by the manufacturer, machine designer/OEM, and user, because there is no thermal device that can protect a motor against a fast transient event. For just as there is a time lag between the final steady-state temp rise of a coil of wire with a given current going through it, there is a time lag for the thermal device to achieve its trip resistance once that trip/application temperature has been presented to the thermal device.
However, the key to answering the question is in the understanding that a thermistor provides its best protection against motor over heating when applied where the motor's utilization is in the 80-90% range of full capacity as sized for an application. Under this condition with proper circuitry there should be no real advantage of one over the other. **
However, there are other considerations; so, why would anyone use a linear thermistor over what has become the industry standard: avalanche PTC/NTC type thermistor?
A linear thermistor offers the user an enhanced capability, if utilized, for maximizing production rate of a given product, by the fine-tuning of a motor's motion profile for it full capability utilization (just within its capacity without overheating, of course). This application of a linear thermistor for enhanced production can be especially helpful with proper programming for machines that often run different size product, like some packaging machines, high speed index machine like sorting, or component placement, etc…
It is seldom one can actually speed up the specific work being accomplished on the item/part without a technology upgrade/change, so all that is left is the possible decrease of the handling/move times between parts or work stations, which translates into higher production rates by higher acceleration, deceleration, and traverse rates.
These potentially higher acceleration, deceleration, and traverse rates, translate into higher energy requirements which in-turn will cause more losses and more heat. It is here that the linear thermistor can help, if so utilized. For its linear resistance as a function of temperature allows for a more actuate repeatable temperature reading and prediction, of the motor's temperature under a specific condition and/or motion profile change (increase) without going over the motor's continuous capability at a specific rms cycle speed; where the avalanche style thermistor is designed to look like a short (low resistance) under a specific temperature and an open (high resistance) at and above, that specific temperature. Consult Graph [below].
Thus with the avalanche style thermistor, it is very hard to get an accurate representation of a motor's temperature as it approaches the motor's continuous capability and even harder to predict its reading for a potential motion profile change due to its resistance slope as the measured temperature approaches the motor full capability. In addition, remembering what an avalanche thermistor was designed for, its slope: resistance vs. temperature, is not necessarily the same from one component to the next.
Hence the utilization of a linear thermistor versus an avalanche type, for a more accurate monitoring of a motor's temperature during a given product manufacture and motion profile, can help the OEM/user acquire long term temperature data acquisition (for dynamic monitoring and fine-tuning/correction, of a specific product's manufacture and ambient temperature), which in turn can be utilized to enhance product rates and at the same time minimize motor potential overheating and machine down time.
In other words, the linear thermistor presents the possibility of enhanced production rates by the accurate monitoring of individual motor temperatures for a given motion/process, with the fine-tuning of each motion for the process being performed, by an automatic venue/program or by a physical human interpreting data.
** A drive algorithm is likely a better solution for the motor's protection during the event of an overload from a low or ambient temperature.