A computer determines a thickness and/or a temperature of a metal strip. The computer determines the temperatures occurring along a respective rotation part of the respective surface elements of the rotary elements and a rotary element shape which forms in the region of a draw-off point on the respective surface element, by a respective rotary element model and using an exchanged enthalpy quantity, the respective contact time with a metal and a respective cycle time exchanged per time unit of a respective rotary element of a casting device with the environment thereof. The temperature of the metal situated in the die region, and the heat flow from the metal to the respective surface element, are determined by a respective metallurgical solidification model and using a metal temperature, the temperatures of the surface elements, the rotary element shape and characteristic metal values.