Most materials expand when heated. As long as the temperature change is sufficiently small, each dimension of an object expands according to:
ΔL = LoαΔT or L = Lo (1+αΔT)
where Lo is the original length.
The length change is proportional to the temperature change.
Here α is the coefficient of linear expansion.
Correspondingly, the volume expands according to:
V = [Lo (1+αΔT) ]3
= Lo3(1 + αΔT)3
≈ Vo (1 + 3αΔT)
≡ Vo [1 + βΔT]
where β = 3 α is the coefficient of volume expansion.
An important counterexample: water!! Water is denser than ice! This effect: