The author examines the conditions in which quasi-steady operation of a thermonuclear reactor is possible. The examination is based on the equation for the energy balance of a deuterium-tritium plasma layer in which thermonuclear reactions are occurring. It is assumed that the principal energy losses from the system are due to thermal conductivity of the plasma and to bremsstrahlung. It is shown that quasi-steady operation of a thermonuclear reactor, requires certain limitations on the transverse plasma dimension L. When this dimension exceeds a critical value Lmax, there will occur self-acceleration of the thermonuclear reactions and self-heating of the plasma, which in the initial stage are similar to a thermal explosion. If L < Lmin, the energy lost from the system will exceed the energy released in it and the thermonuclear reaction will be extinguished. The quantities Lmax and Lmin are determined by the transverse transport coefficients of the plasma and by the boundary conditions.The temperature distributions in the plasma layer are found. The author analyses the stability of these distributions and concludes, in particular, that steady states are unstable in systems with a low boundary temperature.