For fast transient temperature I typically prefer the use of thermocouples. As U. Dreher mentioned, the smaller the "thermal mass" of a sensor (e.g. physical dimension), the faster the response. Thermocouples can be made really small with temporal response in the microseconds.
Thermocouples in general also have a wider dynamic range compared to thermistors, with the former having a linear response to temperature, whereas in the case of thermistor you'd need to linearize the response with a Wheatstone bridge circuit. Thermistors can also have self-heating issue because it is a resistive element.
For accurate measurement with thermocouple, cold junction compensation may be required. But the hassle is worthwhile because you will get good dynamic range, accuracy and fast transient response.
Mass of thermistor is certainly higher than the mass of the bi-metal junction of any thermocouple, hence thermocouple would be faster than thermistor. But commercial thermocouples would have a body that would contribute more mass than thermistor amounting to much less response time. Simply use bimetal wires twisted to get fast response (unless the setup requires it enclosed in a case)
Yes agreed. Best is to fuse your own thermocouples to get the smallest bead possible. But then one is now forced to design his or her own cold junction compensation.
About the cold junction compensation, just keep one more junction in series (one as sensor and the other for compensation). Possibly connect the thermocouple wires directly to the instrument to avoid too many kinds of metal junctions (even though all bi metal junctions can not be as good as thermocouple wire metals, they could contribute to errors).