How hot should water be to brew ground coffee directly in a cup? I don't have a coffee press so I just brew ground coffee as you would tea: in the cup. 

How hot should be the water to brew with this method? Should it be boiling, or a lower temperature?
Your method most closely resembles Turkish Coffee, which is suggested to be served at hot, but not boiling temperatures. Since the exposure to the grounds is so direct, it's easy to burn the coffee at boiling temperatures. You want a full body, but not a burnt taste (yuck!) Turkish Coffee World recommends about 158 degrees Fahrenheit or 70 degrees Celsius.