In this article, we present quantum chemical density functional theory (DFT) calculations of the NMR (13)C chemical shift (CS) tensors in 2,3,6,7,10,11-hexahexylthiotriphenylene (HHTT). The DFT calculations are performed on a smaller model molecule where the hexyl chains were reduced to methyl groups (HMTT). These tensors are compared with our previously reported experimental results carried out under magic-angle spinning (MAS) conditions. The phase diagram of HHTT is K <-> H <-> D(hd) <-> I, where H is a helical phase and D(hd) is a columnar liquid crystal. The motivation for the present study was to explain experimentally observed and puzzling thermal history effects, which resulted in different behavior in the helical phase upon cooling and heating. In particular, the CS tensors for the aromatic carbons measured in the helical phase upon heating from the solid phase were essentially unaffected, while the cooling from the columnar liquid crystal resulted in a significant averaging. We investigate the effect on the CS tensors of (i) conformational transitions, and (ii) relative molecular orientations within the columns for dimer and trimer configurations. Finally a motional wobbling (PIZZA) model for the dynamic averaging of the CS tensor in the helical phase is suggested.