The temperature dependence of nuclear shieldings as well as isotope effects on shieldings and spin-rotation constants have been computationally investigated for H2, HF, F2, CO, and N2 employing the coupled-cluster singles and doubles (CCSD) method augmented by a perturbative treatment of triple excitations (CCSD(T)) for the calculation of potential curves, shieldings and spin–rotation functions together with finite-element techniques for the solution of the rovibrational problem. Calculated and measured temperature dependence of the isotropic shieldings agrees for N2, while for CO and F2 the computed temperature dependence is smaller than the experimental result. Isotropic shieldings have been deduced on the basis of our calculations from the measured spin-rotation constants for four isotopomers of H2 and agree, as required by theory. However, calculated and measured temperature dependence of the isotope shifts between HD and D2 differ by up to 10% which is larger than the estimated error bars for the experimental values. For HF and CO, calculated and measured isotope shifts agree, while for N2 no experimental data for comparison are available. In case of spin–rotation constants, the calculated dependence on the rotational angular momentum quantum number are for both H2 and F2 in good agreement with the dependence deduced from measurements, while for HF not enough experimental data are available for a comparison.