It is demonstrated the high thermal sensitivity of fiber Bragg grating with polymer jacket. Twenty-three times enhanced sensitivity and over 41nm Bragg wavelength-tuning range have been obtained when the fiber grating is packaged with a special kind of polymer. This is the largest thermal sensitivity and largest temperature-tuned range ever demonstrated to our knowledge. It is demonstrated the high thermal sensitivity of fiber Bragg grating with polymer jacket. Twenty-three times enhanced sensitivity and over 41nm Bragg wavelength-tuning range have been obtained when the fiber grating is packaged with a special kind of polymer. This is the largest thermal sensitivity and largest temperature-tuned range ever demonstrated to our knowledge.