The availability of nonlinear parametric processes, such as frequency conversion in photonic integrated circuits is essential. In this contribution, we demonstrate a highly tunable second-harmonic generation in a fully complementary metal-oxide-semiconductor (CMOS)-fabrication-compatible silicon nitride integrated photonic platform. We induce the second-order nonlinearity using an all-optical poling technique with the second-harmonic light generated in the fundamental mode, and a narrow quasi-phase matching (QPM) spectrum by avoiding higher-order mode mixing. We are then able to broadly tune the phase-matched pump wavelength over the entire C-band (1540 nm to 1560 nm) by varying the poling conditions. Fine-tuning of QPM is enabled by thermo-optic effect with the tuning slope Δλ/ΔT in our device being 113.8 pm/°C. In addition, we exploit the measurable variation of the 3 dB QPM bandwidth to confirm how the length of the all-optically inscribed grating varies with exposure time.