The direct driving route would probably take you through Extremadura, one of the least-visited pockets of Spain. I spent several days in Caceres, which has a very well-preserved walled medieval district, and made side-trips to Trujillo (also with a picturesque walled old town) and Merida (impressive Roman ruins, second only to Tarragona in Spain). I know nothing about the November weather in that area. It's quite hot in the summer, but so is Madrid, and Madrid's winters are cold. Extremadura would be quite a contast to the big cities of Madrid and Lisbon.
On the Portuguese side of the border, you'll be passing very near the walled town of Evora. I've never been there but it's often recommended.