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We analyze numerically the use of a tapered Yb-doped fiber to explore the temperature response of fiber amplifiers and their feasibility to be used as a sensing element in temperature fiber sensors. The impact of using different pump schemes and different longitudinal shapes of the tapered doped fiber is investigated, and we found that a parabolic shape of the taper and the co-propagating pump scheme are more sensitive to temperature changes at low pump powers. Our results can be used to describe the temperature response of tapered fiber amplifiers doped with other rare-earths, and contribute with new information for the development and optimization of temperature fiber laser sensors.