Not far from Gran Vía, almost behind the Senate you have a classic place to have a nice "cocido", La Bola. Nevertheless, it is rather strange for someone from Madrid to have such a strong and hot dish when it is almost 35º!
Better to ask your hotel to make a reservation. Other places are "La Daniela" and "Lhardy" (the latter more expensive, XIXth decor)
Best regards and enjoy