We present the fabrication and characterization of fiber Bragg gratings (FBGs) in an endlessly single-mode microstructured polymer optical fiber (mPOF) made of humidity-insensitive high-Tg TOPAS cyclic olefin copolymer. The mPOF is the first made from grade 5013 TOPAS with a glass transition temperature of Tg = 135°C and we experimentally demonstrate high strain operation (2.5%) of the FBG at 98°C and stable operation up to a record high temperature of 110°C. The Bragg wavelengths of the FBGs are around 860 nm, where the propagation loss is 5.1 dB/m, close to the fiber loss minimum of 3.67 dB/m at 787 nm.