A highly sensitive long-period fiber gratings (LPFGs) temperature sensor based on dual-peak resonance operating near the phase-matching turning point in chalcogenide fiber is proposed. The Ge-As-Se chalcogenide glasses with a high linear refractive index, large thermo-optic coefficient, and wide transmission window was prepared and characterized for temperature sensors. Combined with PMTP and cladding etching, the temperature sensing characteristics of different cladding modes were examined systematically. The results of theoretical simulation indicated that different cladding modes show relatively high-temperature sensitivities, and the temperature sensitivity of the seventh cladding mode was as high as 9.296 nm/°C operating near PMTP, which is about two orders of magnitude higher than that of the traditional silica LPFGs. Therefore, this temperature sensor with high sensitivity and simplified design can be applied to high-precision temperature sensing.