After rulling out intake leaks, exhaust leaks, and jetting issues, you might consider replacing the Crank Position Sensor. My girlfriends 06 883L had the same problems - running terrible only when good and hot. I had the carb apart several times to check float level and to clean it, but problem persisted. Put in a new crank position sensor, and it has run perfectly for several months now. (I suspect that the crank position sensors had problems because there has been several part number changes on them in the past couple years.)

 

all good suggestions...but my experience, is air cooled motors dont run well hot. The cooler the better...but freezing cold also has performance issues...

My nightster runs great in the morning, but in the 110 degree heat, sitting in traffic, it doesn't do so well. You run into pre-detonation issues, dieseling issues, knocking issues...all kinds of "heat" related issues. It doesn't hurt anything, but I try to avoid running her hard when shes hot. I take it real easy, and try not to let her sit in traffic. I will actually stop somewhere to get a frosty beverage on the way home, to allow traffic to die down, that way when I go home its not so hard on the motor. I have worked on air cooled motors before, and heat is your enemy. My recommendation is to run a really good synthetic oil, one that wont break down under high heat situations, and be gentle on her when shes hot. I wouldn't worry about it, and if you are worried, go get you a oil temperature gauge, keep an eye on it.