I-V characteristics of MgB2 superconductors with different metallic sheaths were measured in the range of voltages from 10−7 V up to 10−1 V at liquid helium temperature and external magnetic fields 4.75–8.0 T. R-T measurements of compared superconductors between 20 K and 300 K were also done, which allows to estimate the conductor’s temperature after quench. Quench power density of MgB2 superconductors with different sheaths is compared and analysed. It was found that the tape with Ni sheath reaches higher quench power density in contrast to Ti sheathed one in entire measured range. The quench properties and transport ability were enhanced with adding high conductive strip of metal stabilization. The effect of the metallic sheaths and additional stabilization on the thermal stability of MgB2 conductors carrying DC currents is discussed.