Designing materials with tailor-made thermal properties is an important challenge in current condensed matter and nanoscience, particularly for the implications on efficient thermal management in electronics and for applications related to energy harvesting such as thermoelectricity. Even more interesting is the possibility to dynamically access different heat conduction states, as it potentially leads to the real-time control of heat flow. Here, we leverage phase-engineering in MoTe₂, a 2D van der Waals transition metal dichalcogenide, showing that the thermal conductivity undergoes a giant increase (∼270% at room temperature) upon the phase transition between the common 2H and 1T′ polymorphs. Our first-principles calculations trace back this very large change to the different effects that four-phonon processes have on the two crystal phases. Importantly, the 2H ↔ 1T′ phase transition is ultrafast and reversible and can be triggered by external electric fields, light absorption, and THz pulses.