This trial examines the feasibility, effectiveness and safety of a combination of radiotherapy (over a period of five weeks) and chemotherapy (with 5-FU or Capecitabine and Oxaliplatin) and 10 fractions of deep regional hyperthermia in patients with primary locally advanced or locally recurrent rectal cancer. Previous pelvic irradiation in case of a local recurrence is not excluded from the trial. The treatment protocol aims on a preoperatively improved tumor regression allowing less aggressive surgery in primary locally advanced rectal cancer and a higher rate of curative resections in heavily pretreated locally recurrent rectal cancers.