I had a 10 mile TT this morning that I totally bombed. It wasn't hot (75 degrees) but the relative humidity was ~95% (Dew point 74). I had a similar experience with a particularily humid 5k last track season.
I can deal with heat. In high school I would often race and do well in 100+ degree temperatures but with little humidity.
So is there any way to run better in humidity? I was well hydrated and had some gatorade a couple hours before.
The first thing with humidity is to accept that you won't run as fast in hot/humid conditions as you will in ideal conditions. Try to keep the perceived effort the same in both cases, and let the times fall where they may.
What I would see in southern California was that people would run 'normally in hot, very dry weather (Santa Ana conditions) and would do OK -- until their systems reached bottom (you feel cool enough as long as you can sweat a lot) but the body would get out of balance at some point and sometimes it happened very suddenly (last 500m even).
In high humidity it does not seem that hot but you cannot cool by means of evaporation, so unless you are thin and cool enough by radiation, you can have a hard time.
I remember when I moved to San Antonio, Texas. My wife went out for a run in later September when an early 'blue norther' came through and she was flabbergasted because she was running 45 seconds/mile faster than she had been and it felt more comfortable. The flip side is that she had to slow 45 seconds/mile to adequately cope with the heat load of the high dew point. (I have wondered if it is actually worse to run in 76 degrees and 76 degree dew point than in 78/76 because the cooling mechanism is not interfered with; someone versed in the area said it is possible and did not know for sure).
Question: was it also sunny so that you were also dealing with radiative heat (and/or if it was later in the day were you dealing with radiated heat from many sources, including NOT getting relief when you go into a shaded/wooded area)?