I went Sept 11th-15th last year and it was awesome! I know people talk about how Sept is becoming more crowded, but I'm a teacher and used to going over breaks from school - I felt like it was relatively empty. Last year Rosh Hoshanah was on a Monday, so I took a 1/2 day Friday and a full day off on Tuesday, and it was one of my favorite trips of all time because the crowds were so low. My husband and I decided we would rather take shorter trips around 3 day weekends in the future rather than travel during spring break/summer break.
It's not like we could walk on Space Mountain at 1 PM, but we had buses to ourselves, any seat we wanted at the pool, and plenty of elbow/walking room. The crowds were also slower to build after rope drop. We rode Soarin' twice in a row with no wait at rope drop one morning. Another morning at Magic Kingdom, we walked onto Splash twice and Big Thunder twice, and we could have continued that pattern until about 10:30 AM had we wanted to. It was definitely warm, but no worse than summer at home. By September, your body is acclimated to heat and humidity, so the weather won't be as shocking as it would be in say, June. (just my theory - no actual science to back that up!)
The only disadvantages of this time were shorter park hours and potential for downpours (we only had 2 or 3 short lived storms over 4 days). We definitely took advantage of EMH when offered since they extended the shorter hours.