In this work, a hybrid sensor based on a section of hollow square core fiber (HSCF) spliced between two single mode fibers is proposed for the measurement of refractive index of liquids. The sensor, with a length of a few millimeters, operates in a transmission configuration. Due to the HSCF inner geometry, two different interferometers are generated. The first, a Mach-Zehnder interferometer, is insensitive to the external refractive index, and presents a sensitivity to temperature of (29.2 ± 1.1) pm/°C. The second one, a cladding modal interferometer, is highly sensitive to the external refractive index. An experimental resolution of 1.0 × 10-4 was achieved for this component. Due to the different responses of each interferometer to the parameters under study, a compensation method was developed to attain refractive index measurements that are temperature independent. The proposed sensor can find applications in areas where refractive index measurements are required and the control of room temperature is a challenge, such as in the food and beverage industry, as well as in biochemical or biomedical industries.