The melting of the snowman will be a result of both radiative and convective heat transfer. The sun will directly pour energy into the snowman as radiative heat transfer (although a lot would be reflected too) and the surrounding air, as it is warmed by the sun or by the ground that the sun shines on will transfer heat via convection.

You could call a snowman who refuses to melt a "resilient snowman" or a "stubborn snowman."

There was No narrator in "The Snowman"

Jimmy Durante was the narrator in Frosty the Snowman

the snowman DIED

frost the snowman