I think you should not directly try to correlate temperature and precipitation together.
Both of them are, in general, determined by location, which represents solar radiation level (related to latitude), altitude, distance to nearby water bodies (source of moisture), impacts of atmospheric circulations and ocean currents, and so on.
Thus there should not exist any global correlation between these two factors.
However, in a certain area, they may be related, and I think there may exist another deterministic factor, e.g. distance towards nearby mountains.