We report a stable, high-power, cw, mid-IR optical parametric oscillator using MgO-doped stoichiometric periodically poled LiTaO₃ (MgO:sPPLT) pumped by a Yb fiber laser at 1064 nm. The singly resonant oscillator (SRO), based on a 30 mm long crystal, is tunable over 430 nm from 3032 to 3462 nm and can generate as much as 5.5 W of mid-IR output power, with >4 W of over 60% of the tuning range and under reduced thermal effects, enabling room temperature operation. Idler power scaling measurements at ~3.3 μm are compared with an MgO-doped periodically poled LiNbO₃ cw SRO, confirming that MgO:sPPLT is an attractive material for multiwatt mid-IR generation. The idler output at 3299 nm exhibits a peak-to-peak power stability better than 12.8% over 5 h and frequency stability of ~1 GHz, while operating close to room temperature, and has a linewidth of ~0.2 nm, limited by the resolution of the wavemeter. The corresponding signal linewidth at 1570 nm is ~21 MHz.