cook, boil
爨 centers on cooking with fire and water, specifically boiling or stewing food. The idea extends to the hearth or stove itself.
爨 is a complex character historically depicting hands placing a pot over a fire in a stove, with 同 possibly contributing sound. The modern form retains the fire 火 at bottom and the stove-like upper structure.
The top part looks like a stove with a pot (同) inside, and the bottom has fire 火. Picture a busy kitchen with wood 林 and hands working over a big fire to boil food.
For サン, imagine the sun (サン) heating a giant stove: the sun's rays boil the pot, and サン echoes the reading.