Throttling (arbitrary frequency limitation of the CPU) happens when a sensor is reading bad, a bad battery is used or battery is absent. The machine becomes slow but not always totally unusable. Youtube video playback can become choppy at higher resolutions, moving cursor halts video, etc... The CPU temperature won't go up in most cases (and the fan will either stay quite low or ramp up fully).
Intel Power Gadget can be used to monitor the power consumption and the actual core clock of the CPU to observe proper boosting behaviour under load. Intel Power Gadget is only available starting from 2nd gen Core CPU. Trying to run it on 1st gen Core will result in an immediate kernel panic. Instead, while it is much less user friendly, the following command can be used in the Terminal to monitor the actual core clock, refreshing every 0.1s:
sudo powermetrics --sampler cpu_power -i 100
The following example is a 820-00165 (MBA 13" 2017 i7) with prime95 torture test starting in the middle of the graph.