Theory: Discretisation of the heat conservation equation with finite differences. Conservative and non-conservative discretisation schemes. Explicitandimplicitsolutionschemesoftheheatconservationequation. Advective terms: upwind differences, numerical diffusion. Advection oftemperaturewithmarkers.Subgriddiffusion.Thermalboundaryconditions: constant temperature, constant heat flux, combined boundary conditions.Numericalimplementationofthermalboundaryconditions. Exercises:Programmingvariousthermalboundaryconditions.Solving the heat conservationequationinthe case of constantandvariablethermalconductivitywithexplicitandimplicitsolutionschemes.Advecting temperature with Eulerian schemes and markers.