The time you are talking is exactly when we went. We picked it because I would rather have cooler temperatures than hot conditions, and I can tolerate the rain. That is exactly what we got this spring, and I would probably do it at the same time of year again. Every year is different of course, but we saw fairly average weather, a little cooler than the normals. Typical temperature early were 40's in the morning, and 60's in the middle of the day. It got warmer as we got closer of course. Make sure that you are comfortable in temperatures down close to the freezing mark for a few hours, because you are likely to see this on the high roads during the early weeks. A long sleeved merino, my fleece, and a wind/rain shell did the trick just fine. Try out your rain gear before you go, because you will get rained on. If you're lucky, it might be five days. If unlucky, it might be 20! We had ten rainy days, but only two (out of 35) where it rained more or less all day. For us, we used a poncho and gaitors, and it was no problem at all.....if not exactly delightful. All that said, for every day that was cool or rainy, we had two that were pleasant, sunny, and warm. And nobody can predict your weather a year in advance. Buen Camino!