In which case, it depends on the type of inhibitor. A competitive inhibitor has a structure similar to the substrate, hence would bind to the active site as well, competing with the substrate for the enzyme active sites, decreasing enzymatic activity. A non-competitive inhibitor binds to the allosteric site of the enzyme, causing a structural change in the enzyme active site shape.
There's a difference between the effects of cold-brewed coffee vs. hot-brewed coffee: because different chemical reactions are achieved at higher temperatures, cold-brewed coffee will have a smoother caffeine effect and overall less acidity, which some people experience as part of the kick..
Caffeine is stable all the way up to its sublimation point, which is higher than the boiling point of water. It will neither sublimate nor decompose so long as there is still any water left. Therefore, hot brewed coffee will have more caffeine than coffee brewed cold. Once it's brewed, storage temperature won't matter, unless the water evaporates significantly, changing its concentration.