Which year were they walking? Was it infamous 2016 with this unusual heat wave when a pilgrim died before Almaden?
At a normal year walking the southernmost part of VdlP in mid September should be similar to walking the meseta part of the
Camino Frances in the summer (which I did this July)
Normally in the second part of September the max temperature in Andalusia part (first stages from Seville) shouldn't be more than 32C/90F and since you go north with every stage the temperature goes down. If you are lucky at the end of September crossing the pass of Bejar (low mountains) before Salamanca you can get some quickly melting snow at night.
I didn't walk this part in September yet but I soon will (God and covid permitting). I walked in October once and it was warm and super comfortable. The days in October are short a bit, it can be dark almost until 8:30 am which for me was weird. Advice for those walking in October: do not pick the grapes thinking you are alone. The vineyard owners hire security guys driving around. They have binoculars and they are not very nice