Final answer:
The factor affecting the metamorphic process that is most likely to cause rapid cooling is low temperature.
Step-by-step explanation:
The factor affecting the metamorphic process that is most likely to cause rapid cooling is low temperature. While high pressure and heat are important factors in metamorphism, rapid cooling can cause minerals in rocks to crystallize quickly and form new structures. This can lead to the creation of fine-grained metamorphic rocks such as slate or phyllite. Low temperature can also prevent minerals from fully recrystallizing, resulting in less dramatic changes in the rock's texture and appearance.