A core feature of intractable conflicts is the tendency to cognitively freeze on existing, pro-ingroup beliefs. In three experiments, conducted in the context of the Palestinian–Israeli conflict, we tested the idea that an external incentive for negotiating peace helps unfreeze cognitions. In Experiment 1, making salient that peace with the Palestinians would reduce the Iranian nuclear threat (an external incentive) led to a process of unfreezing. In Experiment 2, we examined whether collective angst as an emotional sentiment (i.e., concern for the ingroup's future vitality as a temporally stable emotional disposition) moderated the aforementioned external incentive–cognitive unfreezing link. As predicted, external incentive salience promoted cognitive unfreezing, but only among people low in collective angst (i.e., people who are not concerned for the ingroup's future). In Experiment 3, we sought to replicate the results of Experiment 2. However, socio-political forces (i.e., a significant upswing in tensions between Palestinians and Israelis) likely served to freeze cognitions to such an extent that thawing was not possible by the means demonstrated in Experiments 1 and 2. The importance of confidence in a peace process is discussed in the context of efforts to unfreeze cognitions during an intractable conflict.