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The absence of thermal instability in the high/soft state of black hole X-raybinaries, in disagreement with the standard thin disk theory, is along-standing riddle for theoretical astronomers. We have tried to resolve thisquestion by studying the thermal stability of a thin disk with magneticallydriven winds in the $\dot{M}- \Sigma$ plane. It is found that disk winds cangreatly decrease the disk temperature and thus help the disk become more stableat a given accretion rate. The critical accretion rate $\dot{M}_{\rm crit}$corresponding to the thermal instability threshold is increased significantlyin the presence of disk winds. For $\alpha=0.01$ and $B_{\rm \phi}=10B_{\rm_p}$, the disk is quite stable even for a very weak initial poloidal magneticfield [$\beta_{\rm p,0}\sim 2000, \beta_{\rm p}=(P_{\rm {gas}}+P_{\rmrad})/(B_{\rm p}^2/8\pi)$]. But when $B_{\rm \phi}=B_{\rm _p}$ or $B_{\rm\phi}=0.1B_{\rm _p}$, a somewhat stronger (but still weak) field ($\beta_{\rmp,0}\sim 200$ or $\beta_{\rm p,0}\sim 20$) is required to make the disk stable.Nevertheless, despite the great increase of $\dot{M}_{\rm crit}$, theluminosity threshold corresponding to instability remains almost constant oreven decreases slowly with increasing $\dot{M}_{\rm crit}$ due to the decreaseof gas temperature. The advection and diffusion timescales of the large-scalemagnetic field threading the disk are also investigated in this work. We findthat the advection timescale can be smaller than the diffusion timescale in adisk with winds, because the disk winds take away most of the gravitationalenergy released in the disk, resulting in the decrease of the magneticdiffusivity $\eta$ and the increase of the diffusion timescale.

Thermal stability of thin disk with magnetically driven winds