They could re-define it as how long it takes the Obama Administration to spend $9,192,631,770.
It seems to me that this entire relational system still needs to be grounded in one basic physical measure - that is, that somewhere at the very foundation of it all you need that cylinder or yardstick or something - to base it all off of. Otherwise the entire system risks 'floating.' Your question 'at what temperature' is my case in point:
Over time, what we've assumed initially were fixed constants, have tended to turn out to vary under different conditions. Sometimes very esoteric conditions, but nonetheless, they have not proved 'constant' after all. Newtons laws of gravitation compared to Einsteinian relativity is the classic example, but there are plenty of others.
That means that as we develop a relational system of measurements, we need to define each and every property that can influence the measurement (ie., temperature, gravitational attraction, etc.). And we can never be certain that we've got every one of those potential influences nailed down. I appreciate the advantages to the relational approach and think it is a necessary approach for precise metrics, but it all leaves me with a funny feeling in the pit of my stomach.