In the summer, low lying area like Seville and Cordoba will be like walking on the sun. Just be prepared that things shut down in the afternoon and reopen. Nobody is out in mid-afternoon summer heat.

abovetheclouds,
The only reason that I suggested Mérida as an Extremadura base instead of Cáceres is that Cáceres is further north and not on the direct driving route from Alentejo to Sevilla,
since you have 21 nights (or 21 days??) for the suggested itinerary above-
-Lisbon-Alentejo-Extremadura-Sevilla-Córdoba-Granada-Málaga

I personally find the historic quarter of Cáceres more attractive than Mérida, but if you choose to stay in a Parador, the Cáceres Parador parking situation is a bit difficult, somewhat convoluted, complicated.

There are very few spaces at the Parador, and their garage is 300 meters from the hotel. It doesn't make for an "easy in and out".
When you finally arrive at the Parador in the heart of the medieval quarter you're directed to go to the private parking facility down the hill by following their shuttle van, then the attendant transfers you back in this van to the Parador. There is a 19 euro/day parking fee (lower for Amigos members).

I've stayed at both Paradors as well as the very contemporary one in Trujillo. Parking there in its garage was a breeze and easily accessible.

As others have said, the heat in Portugal's Alentejo, Spain's Extremadura and Andalucía can be extreme in June. Just so you can be prepared...

abovetheclouds,
The high is Seville today, October 1, was 33 degrees C (92 F). It can be very warm in Andalucía from May until the end of September, just so you´ll know.

Are there new fast train links between Granada and Seville?

I remember having to drive from Malaga to Granada and then to Seville, which was a long drive but I don’t recall a fast train option then, which was probably 10-15 years ago.

www.renfe.com

There are now 3 daily, direct AVANT trains that don't require a train change--a 2 hr. 30 min. ride, slightly quicker ride now than the Alsa bus.

Thank to everyone who has given their time to try and help. I really do appreciate it.

Before we start to reserve, I have one more question, based on a friends advice of how she absolutely loved northern Spain.

So, if you could choose to do either (all by car), which would you choose?

1. Northern Spain, Extremadura and Andalusia
OR
2. Portugal, Extremadura and Andalusia

Thanks again.

Northern Spain is far from Andalusia.

Might be more tolerable temperature-wise in the summer than Andalusia, though that could mean a lot of cloudy days.

Hi,

We will have a car for the entire time we are on vacation and because we will have close to three weeks, there will be more than enough time to travel the approximate 1,200 km of driving distance if we do northern Spain, Extremadura and Andalucia or the approximate 800 km of driving if we do Portugal, Extremadura and Andalucia.

Thanks

OK, if you don't mind the long drive in the heat of summer.

Depending on the itinerary, if you have a long distance between two places, you might consider returning the car and taking either the train or a flight and then renting again.

It also depends on rental rates, like is a longer rental cheaper than two shorter rentals?

I'm not familiar with Extremadura but both Northern Spain and Andalucia could each take up 2 weeks.

I agree with scrb11 that (usually) much cooler Northern Spain, a drive along the Cantabrian coast from A Coruña in Galicia to San Sebastián in the Basque Country, through Asturias and Cantabria (all of the Cantabrian coast's "Green Spain") without venturing into the Aragón and Catalonian Pyrenees can very easily take up 2 weeks.

For me a good exploration of Andalucía would be a minimum of 2 weeks, but I no longer do it in the summer. Again, the high reached 91 degrees in Sevilla on October 5. It was in the high 80s all of last week.