The temporal histogram model and synthesiser that is presented in this paper statistically models the unique usage behaviour of electricity or hot water usage for individual residential households. These can be used to model behaviour and do simulations for demand management and planning. The model takes into consideration both seasonal variations and weekday differences and the synthesiser autonomously generates hourly synthetic profiles. We use 1,200 household electricity profiles, each spanning over one year, and 77 hot water usages, each spanning at least one month for each season, to obtain the results. The results showed that the model can accurately characterise the usage behaviour for a household and accurately predict future usage. The model also has a novel capability to model the relationship between usages at different times of the day, which further increases its usefulness in city-wide utility planning. This reduced hourly prediction errors by 19.6% for electricity usage and 25.0% for hot water usage when the first twelve hours of a day are known. This model can be used as an effective tool for demand-side management strategies and providing insight into utility planning in cities.