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..
Cold brew is a different beast entirely. While heat helps extract more caffeine, cold brew is typically brewed as a concentrate, with a higher than normal coffee-to-water ratio of between 1:4 and 1:8, compared with a more typical drip coffee ratio of 1:15 or 1:25. This alone leads to a higher caffeine concentration.