We study thermal effects on spin transport along a deformable helical molecule in the presence of chiral-induced spin–orbit coupling. The carrier–lattice interaction is modeled by the well-established Peyrard–Bishop–Holstein model within the Langevin approach to include temperature as a stochastic noise. The carrier–lattice interaction causes the occurrence of polaron states in the molecule. We demonstrate the existence of two well-differentiated spin-dependent polaron transport regimes as a function of temperature. In the low-temperature regime, the spatial separation of the two spin-dependent polaron wave-packets results in a nonzero spin current. On the contrary, the spin current becomes negligible if the temperature of the system is high enough. Finally, we characterize this transition and estimate the critical temperature at which it takes place.