When a non-contact and remote temperature measurement is of importance, several environmental factors must be considered. Of these, two are of crucial importance — the surface emissivity of the observed object and the directional emissivity in the object–sensor relationship. This paper proposes FDEM — a Fuzzy Directional Emissivity Model built with the assumption that the observed surface is cylindrically shaped. The model consists of two submodels — for vertical and horizontal directions separately. The main contribution of this paper is the formalization of a linguistic description of measurement conditions typical for an industrial environment. Additionally, dual linguistic fuzzy modifiers were used to increase the accuracy of the modeled emissivity. Finally, the proposed model achieved up to 40% reduction of RMSE error when used for correcting the temperature measurements of a rotating cylinder. Overall, our model provides a novel and reliable way for temperature readout correction on the entire surface of a drying roller, such as ones used in the papermaking industry. Furthermore, the proposed approach is not only inherently capable of compensating for the position of the camera, but also does it in an interpretable, and hence expert-verifiable, manner.