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In this letter, we have demonstrated continuous-wave single-mode operation of 1.3-mum InAs-GaAs quantum-dot (QD) vertical-cavity surface-emitting lasers (VCSELs) with p-type modulation-doped QD active region from 20degC to 60degC. The highest output power of 0.435 mW and lowest threshold current of 1.2 mA under single-mode operation are achieved. The temperature-dependent output characteristics of QD-VCSELs are investigated. Single-mode operation with a sidemode suppression ratio of 34 dB is observed at room temperature. The critical size of oxide aperture for single-mode operation is discussed.