We report on the continuous-wave (CW) operation of 1D terahertz quantum cascade (THz QC) microlaser arrays working on various bound states in the continuum (BICs). We first created a quasi-BIC state by breaking the inversion symmetry of the microlaser array, which enables flexible control of the radiation efficiency. The optimized multi-periods array exhibits single-mode emission with the maximum output power of 21 mW (at 30 K), and the maximum operation temperature (Tcw) of 45 K. To further increase Tcw, we created a hybrid-BIC state by hybridizing a quasi-BIC generated in a few-periods array and a high-Q surface plasmon polariton mode formed in an unbiased array. The hybridization minimizes the pumping area with no obvious degradation of the threshold current density. The reduced pumping area, together with the discrete distribution of microlasers, significantly decreases the device thermal resistance. Such scheme improves the Tcw up to 79 K with a low beam divergence of 17°×17°, and the output power remains 3.4 mW at 20 K. Our work provides a novel solution to control the output power, the operating temperature, and the beam quality of THz QC lasers in CW mode.