Consider the grid (one or two dimensional) of cells modelling the solid - each cell holds the current temperature and heat capacity.
Propagation of heat is then modelled in two iterative steps:
1. Compute temperature differences between neighbour cells thus yielding the heat flux according to the Fourier's law
2. Compute the termperature changes of cells according to heat capacity of a cell
3. Proceed to next iteration of time
This kind of approach can lead to oscillations (which cannot happen under heat transfer equation) - when temperature differences are high, heat is transferred too much between cells so they become to have the temperature gradient in reverse direction.
How to avoid such oscillations?