Absolute temperature sensitivity (S-a) reflects the precision of sensors that belong to the same mechanism, whereas relative temperature sensitivity (S-r) is used to compare sensors from different mechanisms. For the fluorescence intensity ratio (FIR) thermometry based on two thermally coupled energy levels of one rare earth (RE) ion, we define a new ratio as the temperature-sensing parameter that can vary greatly with temperature in some circumstances, which can obtain higher S-a without changing S-r. Further discussion is made on the conditions under which these two forms of temperature-sensing parameters can be used to achieve higher S-a for biomedical temperature sensing. Based on the new ratio as the temperature-sensing parameter, the S-a and S-r of the BaTiO3: 0.01%Pr3+, 8%Yb3+ nanoparticles at 313 K reach as high as 0.1380 K-1 and 1.23% K-1, respectively. Similarly, the S-a and S-r of the BaTiO3: 1%Er3+, 3%Yb3+ nanoparticles at 313 K are as high as 0.0413 K-1 and 1.05% K-1, respectively. By flexibly choosing the two ratios as the temperature-sensing parameter, higher S-a can be obtained at the target temperature, which means higher precision for the FIR thermometers.