DTU offers a number of summer university courses, which are presented at this webpage: http://www.dtu.dk/english/Education/Guest-students/Summer-University.
The offer includes an intensive summer course on Danish language and culture, which takes place in August before the autumn semester. This course is open to all exchange students, but a maximum of 60 students can attend.
All application forms for the summer university courses can be found here: http://www.dtu.dk/english/Education/Guest-students/Summer-University/Application.