Will rest and core work beat heat and humidity?

Why is it that on the Friday before a race the conditions in the city have to be so perfect? 57° with 45% humidity is ideal but I won't be running in Central Park today (or anywhere else). While I'm sure that running hard the day before a race probably affects my performance on race day, I'm not convinced an extra day's rest helps all that much. I took two rest days before the 2010 Dirty Sock and still struggled mightily at the end. The Great Cow Harbor 10K was a rough ride even though I followed my two day rest policy. However, both of those races occurred on days that were extremely hot and humid and perhaps those factors trumped the benefits of resting.

The two best races that I ran in 2010 were the Hope for the Warriors 10K and the Long Beach Turkey Trot 10K. These races were run in cooler temperatures than the Dirty Sock and Cow Harbor 10K's. In both cases I rested two days before and did a 20 minute core workout the day before each race. I won't fool myself into thinking the core exercise made the difference but it may have helped. Weather predictions for Sunday are showing high 50's to low 60's with relatively high humidity and possible thunderstorms. I can't control the weather but I can control my training, so I'll do my core workout and leave the rest to nature.