Hi Pituco,
Personally, I only know of a place where you can rent an appartment short term, but there are many others downtown Madrid.
The place I know of is called Apartamentos Centro norte and they are located at c./ Mauricio Legendre, only 300 metres away from Chamartin Train and subway station. In the Paseo de la Castellana area.
I can get you the phone number, if you are interested.
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Life is not fair, it is only fairer than death
William Golding