Nthe experiment, we examined the melting points of naphthalene and phenol. which factor contributed the most to the difference between the melting points of the two compounds?

Answer is: the greater size of the naphthalene molecule.
Naphthalene (C₁₀H₈) has melting point 80°C and phenol (C₆H₅OH) has melting point of 40,5°C. 
Naphthalene has greater molecular mass (128,17 g/mol) and greater size than phenol (94,11 g/mol).
The melting point of solid is defined as the temperature at which the solid exists in equilibrium with its liquid under an external pressure of one atmosphere.