If the weather is the deciding factor, I guess you'll need to look at the regional forecast when you start and see how far you need to go to have more comfortable temperatures.
Check out the planning tool on godesalco to get an idea of stages. -
Perfiles altitudinales, planificaciĂłn de etapas y archivos GPS para la VĂa de la Plata.
godesalco.com
You'll see that there's a >30km stage to Almaden - the longest stage on the Camino. If you find that you're struggling in the heat and you aren't confident about longer stages, Almaden would probably be a logical starting point (or Zafra). Then you can allow yourself to walk shorter stages.
As you look at the weather map, you should check the temperature in Merida - the former Roman capital, with splendid Roman ruins. I guess it might be cooler than the southern end of the VDLP. It would be a shame to miss it and I think it's a decent city to start from. It's a spectacular city in its own right and the stages from Merida to Caceres are nice. (I have heard that the way into Merida on the VdlP is not so pleasant).
A couple of days further along from Merida, is the city of Caceres - a beautifully preserved medieval city. The way out of Caceres takes you along a busy road. So if you're skipping stages and looking for an optimal place to start, I'd suggest Casar de Caceres - a few km after Caceres.
Public transportation from Seville to places on the VDLP is by bus. The express trains out of Seville run diagonally toward Madrid (via Cordoba and Ciudad Real). They don't follow the VDLP northward. If you find that the weather forecast on the VDLP is really not to your liking, you could, conceivably, take the train from Seville to Madrid and join the Camino de Madrid instead.