Fact #1: Kirins most likely have abnormally high internal body temperatures, since Kirin all have magical fire abilities and fire elementals always have high body heat in cartoons.

Fact #2: The reason mammalian testicals hang outside the body is because sperm begin to die if they get too hot. High body heat = kills sperm.

Conclusion: To counteract their own body heat, Kirin males all have very prominent, bodacious, and colossally large testicals. The Kirin will produce large volumes of genetic material when orgasming. This is all necessary to ensure enough sperm survives to fertilize their dames.