We present a study of the of thermal transport in thin single crystals of iron-intercalated titanium disulphide, Fe$_{x}$TiS$_2$ for $0leq x leq 0.20$. We determine the distribution of intercalants using high-resolution crystallographic and magnetic measurements, confirming the insertion of Fe without long-range ordering. We find that iron intercalation perturbs the lattice very little, and suppresses the tendency of TiS$_2$ to self-intercalate with excess Ti. We observe trends in the thermal conductivity that are compatible with our ab initio calculations of thermal transport in perfectly stoichiometric TiS$_2$.
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