This study investigates the thermal and mechanical behavior of isolated protein microtubules, which are critical bio-beam structures and integral components of the cytoskeleton in eukaryotic cells. By modeling microtubules as beam elements, this research captures their dynamic properties with enhanced accuracy. The equation of motion is developed alongside parametric analyses to evaluate the effects of shear deformation, thermal variations and length-scale parameters on microtubule behavior. The results are compared to classical models and existing literature, revealing superior precision and stronger alignment with experimental observations. These findings underscore the efficacy of the proposed framework in capturing the complex mechanical behavior of microtubules under varying conditions.