PhD student working for ESA (ESOC) from april to julie

My name is Jose Manuel Montilla. I am an aerospace engineer PhD student from Spain and I am going to work in ESOC (an European Space Agency facility in Darmstadt) under ‪Jan Siminski‬ from 15th of april to the 28th of julie. I am looking for a place to stay during that time. I have never lived in germany, so I may be wrong by expecting to rent an apartment for 3 and a half months (or 4 if half a month is not an option). Another question is related to the Schufa (request now) , but If I understand correctly it is fast to get one. So if you tell me that it is possible for me to live in your apartment during april-july, then I will get it to prove my solvency.

Thank you.