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Intercomparison studies of models simulating the partitioning of energy over urban land surfaces have shown the heat storage term is often poorly represented. In this study, two implicit discrete schemes representing heat conduction through urban materials are compared. We show that a well-established method of representing conduction systematically underestimates the magnitude of heat storage compared with exact solutions of one-dimensional heat transfer. We propose an alternative method of similar complexity that is better able to match exact solutions at typically employed resolutions. The proposed interface conduction scheme is implemented in an urban land surface model and its impact assessed over a 15-month observation period for a site in Melbourne, Australia, resulting in improved overall model performance for a variety material parameter choices and aerodynamic heat transfer parameterisations. The proposed scheme has the potential to benefit land surface models where computational constraints require a high level of discretisation in time and space, for example at neighbourhood/city scales, and where realistic material properties are preferred, for example in studies investigating impacts of urban planning changes. [ABSTRACT FROM AUTHOR]