We derive thermomagnonic torque and its "β-type" dissipative correction from the stochastic Landau-LifshitzGilbert equation. The β-type dissipative correction describes viscous coupling between magnetic dynamics and magnonic current and it stems from spin mistracking of the magnetic order. We show that thermomagnonic torque is important for describing temperature gradient induced motion of skyrmions in helical magnets while dissipative correction plays an essential role in generating transverse Magnus force. We propose to detect such skyrmionic motion by employing the transverse spin Seebeck effect geometry. Introduction. Out-of-equilibrium effects involving spin are essential to understanding many spintronic discoveries, such as spin-transfer torque [1][2][3][4], spin pumping [5,6], and the spin Seebeck effect [7][8][9][10][11]. These discoveries enabled unprecedented degree of control in magnetic informationstorage devices in which the magnetization can be flipped at will [12] or the domain wall can be moved in order to change the magnetization configuration [13]. Sizable coupling of spin to thermal flows [14] leads to yet another knob by which we can control magnetization and magnetic textures such as domain walls [15][16][17][18] [25], where the magnetization dynamics have low dissipation as coupling to electron continuum is absent [18,26]. At the same time, even at relatively low temperatures, thermal magnons have very small wavelength and thus can be treated as particles on the scale of magnetic texture [18,27]. This brings a lot of analogies to magnetization dynamics in metallic systems where the dynamics can be controlled by flows of electrons [28][29][30][31]. In conducting materials, on the other hand, thermoelectric spin torque can also couple magnetization to heat flows even in the absence of charge flows [15,22,32].A skyrmion is an example of a magnetic texture that can arise in helical magnets due to inversion asymmetry induced Dzyaloshinsky-Moriya (DM) interaction [33] as observed in bulk samples of MnSi by neutron scattering techniques [34]. Skyrmion crystal (SkX) is particularly stable in twodimensional (2D) systems or thin films as was predicted theoretically [35,36] and later confirmed experimentally [37,38]. Just like other textures, such as domain walls, skyrmions can be manipulated by temperature gradients [39,40]. However, many aspects related to interaction of magnon spin currents to magnetic textures are still unclear [41,42].In this Rapid Communication we address the dissipative β-type corrections to magnonic spin torques. Such corrections play an important role in domain wall dynamics [28][29][30][31]; however, they were introduced only phenomenologically in relation to magnonic torques [18,42]. Here we derive