Structural, energetic and thermodynamic properties of CoAl2O4 and Co2AlO4 spinels are investigated using the density functional theory formalism. Thermal effects are incorporated by means of a non-empirical quasi-harmonic Debye-like model that allows us to study the influence of temperature on the relative stability of different cation distributions over tetrahedral and octahedral interstices of the oxygen sub-lattice. Our simulations are able to reproduce the experimentally observed trend of preferring a greater cationic disorder in CoAl2O4 than in Co2AlO4. This behavior can be explained as due to the higher average charge (smaller size) of the cobalt ion in Co2AlO4 (+2.5) than in CoAl2O4 (+2). According to our calculations, pressure and temperature enhance the preference for structures with Al3+ in tetrahedral sites (and Co2+ at octahedral sites).