A tube reactor for heterogeneous catalyzed gas phase reactions having a thermal tube with a catalyst material around which a fluid heat transfer medium, a temperature-sensitive optical waveguide surrounded by a capillary tube that extends into the catalyst material and has measuring points having a predetermined spacing between adjacent measurement points, and can be connected to a source for optical signals and to an evaluation unit (31) for optical signals reflected by the optical waveguide. The optical waveguide has measuring points having a spacing between adjacent measuring points in the axial direction of the thermal tube which is 0.8 to 5 times the shortest edge length of all imaginary cuboids which, having a minimum volume in the cases in which nominal external dimensions are associated with particles of the catalyst material.