There is no simple, general rule for judging the melting points of compounds
The trouble with judging melting points is that solids have a wide range of different chemical structures. Some are covalent solids made from infinite networks of covalent bonds (alumina, graphite) some are essentially ionic salts (sodium chloride, copper sulphate) some are made from neutral molecules (freebase cocaine, candle wax) and so on. It is the structure that really determines the melting point.
Within a given class (say ionic solids) there may be some generalisable rules (alkali metal halides might show some explicable trends based on ion size, for example). But given a formula and no knowledge about the structure there will not be any rules that are helpful.
Alumina is a solid best thought of as an infinite network of covalent bonds; common salt is an ionic solid consisting of sodium and chloride ions. Alumina is a refractory and strong solid because of this structure, with a very high melting point. Common salt has a high melting point but is much lower than alumina. Some ionic salts with large floppy ions are liquid at room temperature.
The forces holding the solid together determine the melting point but you need to know the structure before you you know what the key forces are. Covalent bonds are strong in covalent network solids. Ionic bonds are not as strong but are still far stronger than the forces that hold together discrete molecules in molecular solids like candle wax or menthol. Knowing the structure tells you a lot; knowing the formula doesn't (always) tell you what you need to know.