The particle model of matter
All matter is made of tiny particles that are always moving with space between them, and heating makes them move faster.
A worked example
A gas squashes into a smaller space because its particles are far apart. A liquid barely squashes, because its particles are already touching.
The mistake people actually make
Heating does not make the particles themselves bigger or heavier. They move faster and spread further apart, and that is what makes the object expand.