Bonjette is confusing melting and boiling points with molecular stability. Double bonds are harder to break, but melting does not usually involve breaking covalent bonds.

For 2 molecules with the same number of carbon atoms, and the same structure, the one with double bonds will melt lower.

There are two reasons I know of.

Firstly:
Each double bonded pair of carbons has only 4 groups bonded to it, while single bonded pairs of carbons can accomodate 6 groups. So double bonds lower the molecular mass.

Secondly:
The 4 groups bonded to a pair of double-bonded carbons are arrayed in a planar fashion, while the 6 groups bonded to a pair of single-bonded carbons are arrayed in 3 dimensions.
So, molecules with double bonds are less tangled and melt lower.

This same principle applys to boiling points.