Look a little closer
Road salt does not melt ice by being hot. Dissolved salt lowers water's freezing point below 0°C, making liquid more favorable than solid at the same conditions.
Even below 0°C, an ice surface can support an extremely thin liquid-like layer. Salt crystals dissolve into this water and separate into sodium and chloride ions, creating brine.
Growing pure ice requires water molecules to join an ordered crystal lattice. Dissolved ions change water's chemical state, making that lattice less stable at a given temperature. This is freezing-point depression.
If the surroundings are warmer than the brine's new freezing point, some ice melts to establish equilibrium. Melting draws energy from the ice, road and air, so an ice-salt mixture can actually become colder. The same principle chills an ice-cream container.
Salt does not work equally well in every condition. With little available water or at very low temperatures, melting becomes slow, and sodium-chloride brine itself cannot remain liquid below a limiting temperature. Road crews may choose other deicers accordingly.
Salt is therefore not a heating agent attacking ice. It is a solute that changes the solid-liquid balance: it dissolves in a surface film, lowers the freezing point and allows more ice to become liquid.
