Lightweight aggregate concrete (LWAC) combines low density with high thermal insulation capacity, offering clear advantages for reducing heat transfer through building components. This work investigates LWAC mixtures including cement replacement levels with a silica-rich micrometric by-product from dunite mining, which may further decrease the effective thermal conductivity of the composite material. Nevertheless, the heterogeneous microstructure of LWAC leads to a complex thermal response that cannot be reliably described using conventional homogenised models. At the mesoscale, heat transfer is governed by the size, spatial distribution, and thermal properties of lightweight aggregates within the cementitious matrix. Therefore, mesoscale modelling becomes essential to accurately predict the effective thermal conductivity of LWAC. This work presents a three-dimensional mesoscale numerical framework to evaluate the effective thermal conductivity of LWAC for multiple mixture designs. The material is modelled as a composite consisting of a cementitious mortar matrix and randomly distributed spherical lightweight aggregates. Three mixtures are analysed: a reference mix and two mixes incorporating partial cement replacement of 5% and 10% using a silica-rich by-product derived from dunite mining. Aggregate size distribution is obtained from sieving tests and fitted using the Rosin–Rammler function. A MATLAB routine is developed to generate Representative Volume Elements (RVEs) through a take-and-place algorithm. These RVEs are imported into a finite element environment to perform steady-state heat transfer simulations. The mortar thermal conductivity is experimentally measured using a modified transient plane source method, while aggregate properties are obtained from manufacturer data. Numerical predictions are validated against experimental results from LWAC specimens tested with the same technique.