Using natural water sources like rivers, lakes, canals etc. to remove heat from heat pump or air-conditioner systems is a good practice in terms of improving the system efficiency and running costs. However, the rise of water temperature due to the discharge of heat could potentially impact on the near-by environment and animals. In order to minimise the impact, measures have to be taken to make sure the discharge complying with the regulations. Currently, this is done case by case, which is accurate but time consuming. A general and reliable model of thermal discharge is a useful tool for this purpose; however, this has not yet been sufficiently developed. This study is a step towards this direction and develops an exact solution through applying the advection-diffusion equation for temperature with the known boundary conditions. By assuming that the thermal diffusion in the canal is similar to plume diffusion in the river, the general equations of both vertical and transverse turbulent diffusivities were found from the combination of Manning’s equation and Fischer’s common formula. A Matlab model based on this has been developed and the solution from this model was verified by the referred experiment data with 3-5% difference. The results from the exact solution show that the major influence factors to the thermal diffusion in the canal are the ground friction, the hydraulic radius and the depth of the canal. They influence the turbulent vortices and eddy in vertical and transverse directions through shear forces. Meanwhile, the variation of velocity of discharged warm water in the turbulent range is unaffected to the temperature decay when is higher enough to reach the maximum limit of turbulent diffusion on its specific canal condition.