Hot water effectively removes the coffee-flavoring solubles. Brewing water at cooler temperatures for the same amount of time will result in a lighter extraction and will result in a flat taste. Alternatively, brewing at a temperature range that is too hot will result in bitter coffee.
For manual brewing methods, it is recommended to use an average temperature between 195-205 degrees Fahrenheit (91-94 Celsius). Although the temperature can be approximated by pouring a couple minutes after it reaches a rolling boil (212 degrees Fahrenheit - 100 degrees Celsius), using a thermometer will remove all guess work. Also note that boiled water removed from heat will lose approximately 1 degree Fahrenheit every 15 seconds. For this reason, you'll want to start on the upper range of temperatures which then factors in the cooling during the pouring process. Do not put boiling water onto coffee as this will actually burn the grounds. Another tip is to use hot water to warm up the brewing vessel, cup, and other equipment to help slow down the cooling process during preparation.
For pour-overs, the water level of the coffee bed greatly impacts the temperature during the extraction process. Keep the level low will help slow down the flow rate and will help maintain a more consistent temperature as the water passes over the coffee. A high level will drain too fast and dissipate the heat too quickly - this is not desirable.
Always remember, coffee is only as good as its weakest link. Compared to the other variables, temperature can be more difficult to control. Do not stress if the temperature is not exact to the degree but do ensure that it falls within the range given above.