We study the feasibility of using decay-time measurements in order to develop a temperature sensor superior to the intensity-based one. We measured the fluorescence output of erbium-doped silica fiber segment upon pumping with 980-nm radiation. For low pumping powers (from 4 mW to 10 mW, in our case), the fluorescence power increases rapidly with pumping power. At an intermediate pumping power that depends on fiber dopant concentration and fiber geometry, the fluorescence power starts to saturate, approaching asymptotically the saturation value. We also report that the time constant of transition from excited level 4I13/2 to ground level 4I15/2 depends on the pumping power.