The plastics that soften when heat is applied, with or without pressure, but require cooling to set them to shape are called thermoplastics.
Explanation
Thermoplastics are polymer materials that become pliable or moldable at an elevated temperature and solidify upon cooling. This softening and hardening process is reversible, allowing thermoplastics to be reshaped and recycled repeatedly. The polymer chains in thermoplastics associate by intermolecular forces which weaken with heat, making the material soft, and then strengthen upon cooling to set the shape.
Comparison to Thermosetting Plastics
Unlike thermoplastics, thermosetting plastics (thermosets) undergo a curing process forming irreversible chemical bonds, and do not soften upon reheating. Thermosets do not melt when heated again but decompose, thus they cannot be reshaped after setting.
Therefore, the correct term for plastics described in the query is thermoplastics.