Filtering light from a broadband source with a Fabry-Perot etalon generates comb-like peaks in the spectral domain that can serve as calibration reference for precise Doppler shift detection on astronomical spectrographs. Fiber Fabry-Perot etalons are small in size and easily aligned optically. In application, high thermal sensitivity of the fiber core material requires a highly stable temperature control system. Here, we report on the design, characterization, and thermal performance of a fiber Fabry-Perot etalon-based calibrator system insensitive to environmental temperature perturbation, aimed as a reference for m⋅s-1 precision radial velocity measurements. A fast and simple method to estimate the etalon finesse and a dual-loop approach to achieve sub-millikelvin temperature fluctuation are proposed and demonstrated.