Tunable mid-infrared radiation (3.45-3.75 μm) with a power level of 0.14 μW is generated by quasi-phase-matched difference-frequency mixing of a Nd:YAG laser and a tunable-diode laser (near 1.5 μm) in multigrating periodically poled KTiOAsO4. The wavelength and temperature bandwidths are ≈65 nm cm and ≈62°C cm, respectively. The temperature-tuning slope of the phase-matched idler wavelength, -0.94 nm/°C, is almost twice that of periodically poled KTiOPO4. We use the measurements to derive a mid-infrared-corrected Sellmeier equation for the Z axis of KTiOAsO4. The generated mid-infrared radiation is applied to sensitive high-resolution spectroscopy of the ν3 band of methane.