I think Donna's concern is in the South between Sevilla and Salamanca.
The challenge in mid August was to find any relief from the sun. I tried to start walking before dawn to get in some time before the sun came up in force.
I had to do some serious scouting the night before to insure I could find my way in the morning. The VdlP has some issues with markings in many areas and finding them in the dark was not something I excel at. Actually, I have problems in the light
as I tend to zone out and not really pay attention.
I recall the the temp would usually stay in the 30c (90f) at night and by 9 am with full sun the temperature would be in the 40s and 50s and as high as 55c on the asphalt, according to a small thermometer I had and confirmed by the few bike riders that came by. They would almost always stop and check on me and offer water. They were usually carrying large amounts.
The few bikers were mostly young Italians and riding alone. I was very impressed by the concern.
This was for the first couple of weeks. As I said before, it improved as I went North.
I had a problem of my water getting hot and very difficult to drink.
An umbrella was a great relief and I highly recommend you pick one up in Sevilla before you start. A big canopy is wonderful. You are still hot but not being seared by the full sun.
I suggest you will find the conditions much less severe in June.