Higher temperatures mean higher energy levels. At higher energy levels, the average atom separation is also larger. When you increase the temperature for most objects, they expand. Of course, this assumes that the more complicated ball and spring model works for solids as well as for molecular hydrogen, but it mostly does.
There’s this as well, which is a snapshot of how physicists think:
The simple spring model is much easier to use and works for some things. Like all models, if it works we us it.
It explains why we e.g. model things as harmonic oscillators all the time. It works.