We develop a theory for the thermal Hall coefficient in a spin-$\frac{1}{2}$ system on a stripe of Kagome lattice, where a chiral spin-interaction term is present. To this end, we model the Kagome stripe as $3$-leg $XXZ$ spin-ladder, and use Bosonization to derive a low-energy theory which indicates that the system exhibits a quantum phase transition from massive dimer-crystal (DC) to spin liquid (SL). Introducing a temperature difference $\Delta T$ between the top and the bottom edges of the stripe,we then evaluate the net heat current $J_h$ generated along the stripe, and consequently the thermal Hall conductivity $\kappa_{xy}$. We find that the DC/SL transition is accompanied with a drastic change in $\kappa_{xy}$, which we calculate as a function of coupling constants and the average temperature $T$ for both phases.