chemistry intermolecular forcesWatch
Atoms in Aluminium Chloride are linked by a covalent bond. In aluminium fluoride, aluminium and fluorine are linked by an ionic bond. Since ionic bonding tends to be stronger than covalent bonding, it takes more energy to break ionic bonds, hence an higher temperature (more heat) for aluminium fluoride to sublime.
Aluminium fluoride has a giant structure with strong ionic bonds.
Aluminium chloride has a simple structure with very strong covalent intramolecular bonds, but these are not broken on sublimation, it is the weak intermolecular forces (London forces, I think, but I have been drinking) that are overcome on sublimation.