All-optical poling enables reconfigurable and efficient quasi-phase-matching for second-order parametric frequency conversion in silicon nitride integrated photonics. Here, we report broadly tunable milliwatt-level second-harmonic generation in a small free spectral range silicon nitride microresonator, where the pump and its second-harmonic are both always on the fundamental mode. By carefully engineering the light coupling region between the bus and microresonator, we simultaneously achieve critical coupling of the pump as well as efficient extraction of second-harmonic light from the cavity. Thermal tuning of second-harmonic generation is demonstrated with an integrated heater in a frequency grid of 47 GHz over a 10 nm band.(c) 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement