Heat transfer is a key consideration in the development of tritium breeder blankets for future fusion reactors. For solid tritium breeder materials there is a fine balance to be struck between high levels of porosity to encourage tritium release and minimising it to maintain the thermal and mechanical properties. Therefore, in this work we employ molecular dynamics simulations to understand how the introduction of porosity influences the thermal conductivity of lithium metatitanate ceramic breeder material. Our simulations predict that increasing the porosity leads to a decrease in the thermal conductivity which is in good agreement with previous experimental observations. By contrast, we do not observe the increase in the thermal conductivity at high temperatures, that is observed in some experiments. We argue that this increase is a consequence of sintering or some other modification of the experimental sample rather than a fundamental change in the heat conduction mechanism in the crystal matrix.