A compact tunable mode converter device based on the thermo-optically characteristics of liquid crystals (LCs) is proposed and numerically analyzed herein. The proposed mode converter consists of an asymmetric dual-core photonic crystal fiber (PCF) with a highly thermo-responsive LC core. The verification of the proposed mode converter was ensured through an accurate PCF analysis based on the vector finite element method. With an appropriate choice of the design parameters associated with the LC core, phase matching at a single wavelength is available in the important O-band wavelength region. The simulation results showed that high conversion efficiencies between LP01 and LP11 mode are readily achieved over a broad wavelength range from 1278 nm to 1317 nm. Likewise, the tunable capability of the proposed mode converter was evaluated when it was submitted to thermal changes; thus, we evidence the strong thermo-responsive dependence of the operating wavelength, mode conversion efficiency and full-width at the half maximum (FWHM) bandwidth. Finally, the fabrication tolerances of the devices were also investigated. Therefore, the thermo-responsive characteristics of this novel PCF mode converter can be of fundamental importance in the future space division multiplexing technology.