We investigate multiplexing of four highly sensitive Fabry-Perot (FP) microresonators at the tip of a single-mode optical fiber for refractive index (RI) measurements with simultaneous temperature compensation. The individual sensing elements for RI or temperature consist of either open-cavity FP resonators or solid fiber core regions fabricated by diamond-blade dicing of single-mode optical fibers, respectively. The reflectivity of the open resonators is further enhanced by matched dielectric coatings. At the same time, the solid core resonators formed by the fiber pieces between the open cavities are used as thermometers. This allows immediate compensation for temperature cross-sensitivity during RI measurements. The general performance of the sensor is demonstrated by measuring the RI of sucrose solutions, where we use phase tracking of the characteristic Fourier transform components of the backreflected optical spectrum for evaluation. The temperature sensitivity is on average 20±/∘C with an accuracy of 0.01°C, fully sufficient for biomedical applications. Meanwhile, the four RI sensing (open) cavities show high sensitivity of approximately 1160 nm/RIU. Due to the compact size of the sensor, small spatial inhomogeneities of RI can be accurately detected. If the cavities are additionally filled with molecularly imprinted polymers or coated with thin functional layers, they could also be used for the detection of trace substances in biomedical laboratory-on-a-fiber applications.