Fluorescent nanothermometers are positioned to revolutionize research into cell functions and provide strategies for early diagnostics. Fluorescent nanostructures hold particular promise to fulfill this potential if nontoxic, stable varieties allowing for precise temperature measurement with high thermal sensitivities can be fabricated. In this work, we investigate the performance of micelle-encapsulated CuInS2/ZnS core/shell colloidal quantum dots (QDs) as fluorescent nanothermometers. We demonstrate four temperature readout modes, which are based on variations in the photoluminescence intensity, energy, and lifetime and on a specific ratio of excitation efficiencies. We further leverage this multimodal readout to construct a fifth, multiparametric thermometer calibration based on the multiple linear regression (MLR) model. We show that the MLR approach boosts the thermometer sensitivity by up to 7-fold while reducing the readout error by about a factor of 3. As a result, our QDs offer the highest sensitivities among semiconducting QDs emitting in the first biological window. The obtained results indicate that CuInS2/ZnS QDs are excellent candidates for intracellular in vivo thermometry and provide guidelines for further optimization of their performance.