The paper refers to the current field of magnetohydrodynamics, and contains results related to the propagation of weak discontinuities in the case of unsteady flow of a thermally conductive fluid with infinite electrical conductivity. In the paper, basic equations describing the increase or decrease of weak discontinuities along bicharacteristics were derived and solved analytically. In the discussion of this solution, the criterion for the formation of a shock wave was derived and the time required for this was estimated.