What happens if a pure substance is exactly at its melting point?

Answer 1

it "sweats" almost like melting plastic on a Bunsen burner, like how small droplets form just before the whole pen melts.

Answer 2

If a pure substance is exactly at its melting point, it will undergo a phase transition from solid to liquid or vice versa. During this transition, the temperature remains constant until the entire substance has converted from one phase to another.