The temperature dependence of nuclear shieldings as well as isotope effects on shieldings and spin-rotation constants have been computationally investigated for H-2, HF, F-2, CO, and N-2 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 N-2, while for CO and F-2 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 H-2 and agree, as required by theory. However, calculated and measured temperature dependence of the isotope shifts between HD and D-2 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 N-2 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 H-2 and F-2 in good agreement with the dependence deduced from measurements, while for HF not enough experimental data are available for a comparison.