The regimes of thermonuclear burning in self-sustained and driven tokamak reactors using deuterium-tritium plasma with nuclei polarized along the magnetic field are investigated. A comparison is made between the burning regimes in reactors with polarized and unpolarized plasma. In particular, it is shown that the temperature regions that allow stable steady-state thermonuclear reactions are similar for both types of reactors. However, as compared to the conventional case, the driven reactor with polarized nuclei requires higher power levels of neutral injection or radio-frequency heating to achieve the same stable temperature regime. The power multiplication factor, when using polarized nuclei, is unchanged or may be higher due to deterioration of alpha-particle confinement.