Engineering-related surfaces are commonly rough to different extent. In contrast to smooth surfaces, turbulent flows over rough surfaces exhibit enhanced heat and momentum transfer in the near-wall region due to surface undulation. A long-standing research question in this field is how to predict the roughness effect based solely on its topographical properties. In this regard, a large body of research devoted to characterizing roughness topographies has demonstrated that the usage of reduced statistical properties like skewness or effective slope of the surface remains insufficient to recover the overall roughness effect. Having this in mind, we discuss the potential of characterizing the roughness effect on the temperature field based on the roughness height probability density function (PDF) and power spectrum (PS) in the present contribution. Hereby, different types of realistic roughness from various engineering applications are considered. A mathematical roughness reproduction method is utilized to generate artificial rough surfaces based on the realistic PDF and PS. The artificially reproduced surfaces are subsequently compared with their original surfaces in terms of the thermal properties. For this purpose, direct numerical simulations (DNS) of flow over the roughness are carried out in a fully developed turbulent channel flow at friction Reynolds number Re_τ = 500 - 2000 to cover different rough regimes. Successful reproduction of the flow statistics by the artificial roughness surrogates indicates the feasibility of the current roughness characterization/reproduction method. Less than 4% discrepancies in the global flow statistics are achieved. However, the present roughness reproduction framework is shown not applicable for the roughness with strong surface anisotropy.