The Marangoni instability of a horizontal binary mixture layer with a deformable free surface and a solid substrate is investigated under the action of a modulated heat flux. In contrast to a homogeneous liquid, due to thermal diffusion (Soret effect), the modulation of the heat flux creates not only a temperature wave but also a concentration wave, which changes the surface tension. Two cases of the modulation of the heat flux with a zero mean value are considered: (i)
on a free surface and (ii) on a rigid substrate. In both cases, the long-wave instability exists within the established frequency intervals. The dependences of the critical Marangoni number and the corresponding modulation frequency on the separation ratio and the Lewis number are obtained for long-wave disturbances. The fundamental features of case (i), as compared to case (ii), are as follows: the instability domains are located in the lower frequency ranges and the minimum Marangoni number is several times smaller.