We walked that stretch in July 2014. When we are backpacking in America, we always do what you suggest--sit out the heat of the day, then start walking again in the cool evening. I can cover a lot of miles that way even in the mountains because your legs are really fresh again after a four-hour rest.
We tried to do that on the CF. It did not work. It makes finding beds tough, as mentioned by others. But for us the real problem was that it was so hot our feet began to seriously overheat, contributing in part to really bad blisters (the boots also aided and abetted that disaster). We eventually gave up, and left the alburgues in the dark, walking only until 1pm or so. That would get us 25K (even on badly blistered feet) a day, which is a quite respectable pace. Walking again in September 2016 we could walk all afternoon because it was not quite as hot. But in July, just get to an alburgue, wash your cloths (bring one set cotton long-sleeve, long pants for this section (they'll be your alburgue cloths in the wetter, colder mountain sections)--look at Kuhl Kontra Air pants and Patagonia Steersman shirts), marvel at how fast they dry, take a long nap, get up when the sun goes down, eat dinner, go back to bed, wake up at 4am to leave by 5am. YMMV.
Buen Camino,
Jo Jo