So, finally, it is more comparing (often) a DFT structure at OK but having the cell parameters from an experimental structure at 293K to that experimental structure rather than comparing apples and bananas.
:-) That's the nicest tongue-in-cheek statement I've read in the past few months.
Would be time to make the effort to have DFT results at any temperature including the phase transition predictions. I am sure you also dream of that...
To quite an extent, that is possible. Instead of having only the total internal energy U (which DFT gives you), one needs also the temperature dependent entropy S(T). In that way, you have the temperature dependent free energy F(T)=U-T*S(T). If you compute F(T) for every relevant phase, you can determine the phase transition temperatures.
The question is how to compute S(T). Phonons give the largest contribution to S(T), hence you need a full phonon spectrum -- which is surely doable, but time-consuming. Phonons (=harmonic) are a good description only at not too high temperatures, hence you need anharmonic contributions if you are interested is the high temperature range -- again more time-consuming. And if you want/need to include electronic or magnetic contributions to S(T), again more efforts are needed.
So, it's possible, but you need a sufficiently interesting question to justify the computing effort. It's not yet something that can be routinely done, and therefore it is not yet at the stage where it becomes useful to build a database of results.
Stefaan