Hollow plasma channels are attractive for lepton acceleration because they provide intrinsic emittance preservation regimes. However, beam breakup instabilities dominate the dynamics. Here, we show that thin, warm hollow channels can sustain large-amplitude plasma waves ready for high-quality positron acceleration. We verify that the combination of warm electrons and thin hollow channels enables positron focusing structures. Such focusing wakefields unlock beam breakup damping mechanisms. We demonstrate that such channels emerge self-consistently during the long-term plasma dynamics in the blowout's regime aftermath, allowing for experimental demonstration.