We demonstrate the suitability of terahertz time-domain spectroscopy as a non-destructive, contact-free tool to monitor the glass transition in polymers--a core feature of the amorphous phase. Below the glass transition temperature T(g), segmental motions along the polymer chain are frozen due to the lack of free volume between neighboring macromolecules. We show that this transition also reflects in the temperature dependence of the refractive index at terahertz frequencies. Two domains can be identified, which differ in their sensitivity to temperature changes. To verify the proposed approach, we determine the glass transition temperature T(g) of semi-crystalline poly(oxymethylene) (POM) with terahertz time-domain spectroscopy and validate the results by destructive differential scanning calorimetry (DSC) measurements.