You know reaction happens because delta G<0 => delta H is most likely < 0, so heat disfavours exothermic reaction eqm.
Another way I look at it is that evaporating the water might cause the ligand to fall apart, ie you could get anhydrous copper amine ligands in the end(my speculation).
And in crystallisation process, as far as i know, you usually heat them up first, ie to concentrate the solution, then you cool them down. Recrystallisation then involves dissolving this cooled crystal with minimum amount of cold ethanol or other appropriate solvent(depends on experiments) and cool them further in ice bath.