  We derive thermomagnonic torque and its "$\beta$-type" dissipative correction
from the stochastic Landau-Lifshitz-Gilbert equation. The "$\beta$-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.
