Well there is the technical answer and the practical answer to this question.
Is refractive index dependent on temperature? Yes
Variations in temperature do effect the refractive index of compounds. This is largely due to the fact that a materials density and viscosity are dependent on temperature, and changes to these physical properties ultimately influence the refractive index.
Practically speaking the temperature dependence is not very strong. Although you will see changes due to temperature, the changes are not very drastic. Usually many of the economical RI instruments don't actively control temperature. Rather the light source inside heats up the instrument component to a nominal temperature close to 25-30C.
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