The authors consider the possibility of a self-sustaining thermonuclear reaction in a dense plasma (n ≳ 1016 cm3). The pressure of the plasma is contained by walls and the magnetic field only serves to reduce thermal conductivity in a transverse direction. A solution is obtained for the plasma balance equation that makes allowance for radiation losses along the magnetic field, and it is shown that there is no satisfactory solution across a uniform magnetic field. The authors discuss the possibility of a steady-state thermonuclear reaction with a non-uniform magnetic field.