Lattice thermal conductivity is a sensitive probe of distortions of the translational invariance of crystalline materials. Crossplane thermal conductivity, κ(T), was studied by the 3ω technique in superlattices, comprising orthorhombic charge/orbital ordered manganite Pr0.7Ca0.3MnO3 and cubic SrTiO3. The manganite/titanite superlattices show a peak in κ(T) just above the charge order transition temperature TCO∼240K with a pronounced thermal hysteresis. This ordering peak in κ(T) is successively suppressed with decreasing layer thickness. Our results demonstrate a minor effect of the interface density on κ, primarily visible below TCO. In contrast, much higher changes in κ(T) evolve close to TCO, due to interface-induced effects on charge and orbital ordering. Our results suggest that the ordering peak in κ(T) is a result of lattice softening above the phase transition which is modified by thickness-dependent misfit strain.