Rovibrational corrections, temperature dependence, and secondary isotope shifts of the C-13 nuclear shielding in CX2 (X = O, S, Se, Te) are calculated taking into account the relativistic spin-orbit (SO) interaction. The SO effect is considered for the first time for the secondary isotope shifts. The nuclear shielding hypersurface in terms of nuclear displacements is calculated by using a density-functional theory method. Ab initio multiconfiguration self-consistent field calculations are done at the equilibrium geometry for comparison. C-13 NMR measurements are carried out for CS2. The calculated results are compared with both present and earlier experimental data on CO2, CS2, and CSe2. The heavy-atom SO effects on the rovibrational corrections of C-13 shielding are shown to be significant. For CSe2 and CTe2, reliable prediction of secondary isotope effects and their temperature dependence requires the inclusion of the SO corrections. In particular, earlier discrepancies of theory and experiment for CSe2 are fully resolved by taking the SO interactions into account.