“That temperature is hot enough to melt protons and neutrons,”
I’m not sure “melt” is the right word in this context.
It's probably safe to say that the concept is being dumbed dow...um, simplified, for the masses.
What happens when ice melts? In physical terms, the average ambient energy, as measured by temperature, becomes greater than the binding energy of the water molecules, and so they break free of one another.
All you have to do is compare kT to the binding energy. If this is greater than the binding energy of the quarks comprising a proton or neutron, then they do indeed "melt".
And clocks.