re-heat food
燖 centers on applying heat to food again: reheating or warming up previously cooked food.
燖 combines 火 (fire) with 尋, which likely contributes the sound. The character expresses reheating food over fire.
The left side is fire 火, and the right side 尋 looks like a hand holding a pot over a flame. Picture reheating last night's stew over the fire.
For シン, imagine reheating a thin slice of pizza: thin -> シン, and the fire warms it up.