if the fat content is right i.e. 80/20 or maybe 75/25 the burger will still be plenty juicy at mid-well or well. a rare burger with the right fat content won't even be hot enough to have the fat rendered and that's just gross. i used to be into mid-rare borgor because it was a forbidden thing in my metro's health dept but i got over it because it's just not that good. the most important thing to make it taste good is to get a good sear and salt it right (1% salinity by weight i.e. more salt than you probably think)