I don't adjust temperatures. If you try baking at a higher temperature you risk the bottoms or tops of your cookies burning before the middle is fully cooked. Lowering the temperature will cause thin crispy cookies. By lowering the temperature you are allowing the butter time to melt and spread before the dough has a chance to set and bake. Lower temperatures cause longer bake times which will likely dry out your cookies.
If you are wanting to adjust temperatures or baking times, your best bet is to turn the heat up ever so slightly and keep an eye on your cookies. Depending on the type of cookie you are making a higher temperature could yield a softer thicker (cake like) cookie, but I wouldn't say it will make your cookies moister.