Amorphous polymers are known as thermal insulators, increasing their thermal conductivities have not been guided by fully understood physics. In this work, we use molecular dynamics simulations to study the thermal transport mechanism of solid polyelectrolytes, poly(acrylic acid) (PAA) and its ionized forms. The thermal conductivity of PAA increases monotonically with the ionization strength. Although stronger ionization induces larger Coulombic interactions, the Coulombic interaction does not directly contribute to the thermal conductivity enhancement.Instead, it enhances thermal transport through the Lennard-Jones (LJ) interaction. The strong Coulombic force between the counterion and the ionized carboxylic group shifts the LJ force to the stronger LJ repulsive regime, which is mainly responsible for the improved thermal conductivity. Applying a high pressure can further reduce the inter-atomic distance and trigger the thermal transport through the LJ interaction. A thermal conductivity of 1.09 W/m.K can be achieved at 11.2 GPa in an ionized PAA.