One of the more unique (and least Spanish) sights in Madrid is the Templo de Debod. It's a temple that was originally built in 200 BC in southern Egypt, and dedicated to the gods Amun and Isis. After the Spanish helped save some other Egyptian temples in 1968, the Templo de Debod was given as to Spain as a gift, and dismantled and transported to Spain in the 1970s.
We visited the Templo de Debod near the end of February. You can wander around the outside of the temple no matter when you go, but you can't always go inside. The hours are a bit strange if you ask me - do double check them before you go if you want to go inside. Otherwise you may get lucky and find them different than what was posted on the website, as we did, or you might not and just have to see it from the outside.
The temple is near the Plaza de España, and is surrounded by a park, which offers great views of Madrid and the mountains further afield. In fact, it's known as one of the best spots to watch the sun set in Madrid. Because we were often teaching or eating dinner when the sun was going down, we can't actually confirm or deny whether or not it's a great spot, but it's something we'd like to do if/when we return to Madrid in the fall.
D - I always think it's pretty crazy how the ancient Egyptians did all these complex burials and monuments and other things with no concept that thousands of years later their bodies/art/history would be dug up by archeologists, shipped all around the world, and gawked at by tourists and museum visitors with smart phones. It makes me wonder if people might study me or my generation in a couple thousand years (if humans are still around) and what crazy, unimaginable technology they might be using.
Templo de Debod is a quick and free thing to do in Madrid if you have a bit of spare time. I wouldn't add it to any "must-see Madrid lists" or "top ten Madrid" books, but I'd definitely see it if you're spending an extended amount of time in the city, or if you love all things Egypt.