Boiling and melting point of trans- and cis-but-2-ene
Yes . You are right that structural symmetry comes into play .  

Boiling point depends upon intermolecular interactions which over here is more in cis due to its net dipole moment .  The dipole moment enables electronic interactions which hold molecules together .  This shows some general factors of boiling point . Also the below link to the google book covers the structural aspect of a molecule towards b.p on pg47.

For melting points , let me quote Joseph Hornback from Chapter 2.6 Organic Chemistry pg46 (google books) :   


  The shape of a compound is very important and has a dramatic effect on its melting point . More symmetrical molecules pack into the crystal lattice better , allowing closer approach and larger attractive forces , resulting in higher melting points .    


Melting points of alkenes depends on the packaging of the molecules. Alkenes have similar melting points to that of alkanes, however, in cis isomers molecules are package in a U-bending shape, therefore, will display a lower melting points to that of the trans isomers.(source)

Trans 2-Butene has more symmetry than its cis isomer which results in better packing and hence higher melting point .   

For further reading I suggest you visit 'Molecular Shape' over here.