Because I know that is dangerous to walk in Extremadura in May or June;
I have walked in Extremadura three times in May. Twice, I started the Vdlp in Sevilla in early May, once I started the Mozárabe from Almería in mid-April.
I would not say the heat level in May is typically dangerous, but of course things can happen.
I always time my southern starts to try to coincide with peak wild flowers. Those three caminos were jam packed with an amazing wildflower display all along the way.
This year I started in Alicante in mid May, and because of the drought, particularly hard hitting in the south, the wild flowers were not out in force. The fields were not their typical emerald green, there were a lot of failed crops. Further north, there were more and more, but nothing like previous years.
All of this to say, that if your main concern is the heat, I think a later start is still likely to be very do-able. Extremadura in May or June is not likely to be like Extremadura in July, August, or September. Thoughh we know we are losing our grip on what is “normal” when it comes to weather.