There are definitely short term apartments for rent on all the major local housing websites. Try http://bj.ganji.com/fang10/ or http://beijing.koubei.com/fang. Someone could list the multitude of other sites which have escaped my mind.
By default, the "landlords" for short term rentals will be agents, and they're often crooked. Assume in the least that if the place doesn't have an electronic lock then an unlimited number of people have the key and will be visiting you.
But I rented a place at 四惠，东横时代 before for short term which was very nice and had no problems.
Obviously, those daily rates are negotiable if you're staying longer than a couple days.