A tumble dryer has a drum for laundry, a drive motor for the drum, an air supply to the drum and an air discharge from the drum, a fan, including a fan drive, for generating an air stream to the drum through the air supply and away from the drum through the air discharge, and also heating means for heating the air stream. The temperature of and the moisture in the air which is discharged from the drum are detected. The profile of said temperature and moisture is compared with prespecification curves, which are stored in a memory, for the profile of said temperature and moisture by means of calculation means depending on the drying phase of the laundry. The operating point of the prespecification curve at which the drying program is located is determined in this way. The control arrangement influences the further drying program, on the basis of the operating point, by way of adjusting the temperature and/or the intensity of the air stream.