Would you please be more specific? what do you mean internal heat generation, CF and PI? The broader the audience the most likely a solution to your problem will come. You should write down the equation, the boundary conditions and the definitions of the quantity you want to calculate.

All the best,

Fabio

Internal heat generation is a moving heating source, CF is Complementary function, and PI is Particular integral.

There is still insufficient detail! Is this an infinite domain or a finite domain? If there are any boundaries, then what are the boundary conditions. What is the initial condition? If it is a finite domain, such as a cuboid, wouldn't it be better to use Fourier components spatially?