The Archimedean spiral coil made of a transversely corrugated pipe represents the radiant heat absorber of a parabolic dish solar concentrator. The main advantage of the considered design is the coupling of two passive methods for heat transfer enhancement: coiling the flow channel and changing the surface roughness. The aim of this numerical study is to assess the capability of RANS models of different complexity (realizable k-ε, SST k-ω, and RSM linear pressure-strain) to adequately represent the heat transfer phenomena in the considered complex flow geometry for wide ranges of Reynolds and Prandtl numbers. The obtained results indicate that the realizable k-ε model with enhanced wall treatment is inadequate to simulate the heat transfer for all flow conditions, while both SST and RSM slightly overestimate experimental data in the turbulent region and are able to predict laminarisation at low Reynolds numbers. The SST model predictions are more accurate in the transitional and at the beginning of the turbulent region, irrespective of the curvature ratio. The RSM predictions are generally more accurate in the turbulent region. Numerically obtained circumferential distributions of local Nusselt number reveal that considered turbulence models are unable to completely anticipate the interactions between the complex flow in the basic section of the pipe and the vortex flow within the corrugations.