We numerically analyze the temperature response of tapered doped fiber amplifiers and discuss their feasibility to be used as a sensing element in temperature fiber sensors. In particular, we consider Ytterbium (Yb) and Thulium (Tm) rare earths in the tapered doped fiber designs. We have modified the coupled propagation equations for the pump and signal radiations in order to include different taper structures and introduce the temperature dependence of the absorption and emission cross-sections of Yb and Tm ions. It was found that the temperature sensitivity of the amplified signal in Tm-doped fiber amplifiers is one order of magnitude higher than this obtained with Yb-doped fibers. Additionally, in all doped fibers, the temperature sensitivity of the signal radiation is higher for low pump powers in a co-propagating pump scheme, and it highly depends on the longitudinal shape of the taper used. Finally, for both Yb-and Tm-doped fibers, the temperature sensitivity can be increased if we use doped fiber lengths shorter than 1 m and pump powers lower than 300 mW. This study provides valuable information for the development of tapered fiber amplifiers doped with other rare earths and novel designs for doped fiber temperature sensors.