Q:

Thermodynamics cooling curve question

I'm given that a solid is heated, beyond melting point and then the temperature of the liquid is 90 Celsius. When it cools, the temp falls to around 80 Celsius and stays constant for a period of minutes before falling again.
What would 80 Celsius represent here in thermodynamics terms?
Am I  right in assuming it's the temperature just above the solid - liquid phase change on a cooling curve?

A:

Am I right in assuming it's the temperature just above the solid - liquid phase change on a cooling curve?

Not above, but exactly at the solid-to-liquid (or rather liquid-to-solid, also known as freezing or solidification) phase change region:

Considering water, it might start at $10 \;\mathrm{^\circ C}$ and is then cooled down to $-10 \;\mathrm{^\circ C}$. Along the way, there will be a while of constant-temperature cooling at exactly $0 \;\mathrm{^\circ C}$.

