Best Unexpected Travels in Spain!

The northern coast of Spain is typically very nice, weather-wise, in mid-summer. You could go to the Basque Country or to Galicia. If you're the active outdoor type, the Picos de Eurropa would be good, though a multi-day stay in that last area might be very difficult without a car.

I would not add on time in Andalucia; just too hot.

Ibiza in February. Paradise.

I agree with the recommendation for the Basque region. It is very interesting and beautiful plus it won’t be hot like Andalucia. If you decide to travel there read Mark Kulansky’s “ The Basque History of the World” before you arrive.
Save beautiful Seville for another time when you can enjoy it without the intense heat.

In July I would head to the northern Basque Country. Head directly from Salamanca, finishing up in Madrid for your flight home.

The historic centre of Valladolid might make for a nice stopover as well. Situated on the Pisuerga River, it is home to an interesting collection of Renaissance architecture, including the Cathedral, the College of San Gregorio (today the site of the National Sculpture Museum) and the church of San Pablo.
https://m.spain.info/en/destinos/valladolid.html

Day
1. Train (1hr 08min) from Salamanca to Valladolid (1N)
2. Train (3hr 46min) from Valladolid to Bilbao (2N)
3. Bilbao
4. Bus from Bilbao to San Sebastián (2N)
5. San Sebastián
6. Train (5hr 31min) from San Sebastián to Madrid (3N)

I agree with the others; add 5 days and spend it either in the Madrid area or Madrid and further north. There are plenty of great cities and towns worth visiting.

How do you deal with extreme heat? In August, triple digit temps in Sevilla and Madrid are not unusual. You are headed to the hottest, driest part of Europe - great in winter, not so much in summer. Remember, you will be out walking for hours, much of the time with little or no shade.

Thank you so much everyone for your advice. I will save going South to a time the weather is cooler!
KATHY

Thinking outside the box - any interest in jumping on a quick plane over to Paris for your last days? Usually Paris can be a non-stop flight home, also.