Bragg gratings have been written in exposed-core microstructured optical fibers for the first time using a femtosecond laser. Second and third order gratings have been written and both show strong reflectivity at 1550 nm, with bandwidths as narrow as 60 pm. Due to the penetration of the guided field outside the fiber the Bragg reflections are sensitive to the external refractive index. As different modes have different sensitivities to refractive index but the same temperature sensitivity the sensor can provide temperature-compensated refractive index measurements. Since these Bragg gratings have been formed by physical ablation, these devices can also be used for high temperature sensing, demonstrated here up to 800°C. The fibers have been spliced to single mode fiber for improved handling and integration with commercial interrogation units.